Journal of Volcanology and Geothermal Research 200 (2011) 129–142

Contents lists available at ScienceDirect

Journal of Volcanology and Geothermal Research

j ourna l homepage: www.e lsev ie r.com/ locate / jvo lgeores

A statistical approach to evaluate the tephra deposit and ash concentration fromPUFF model forecasts

S. Scollo a,⁎, M. Prestifilippo a, M. Coltelli a, R.A. Peterson b, G. Spata a

a Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Catania, Catania, Italyb Mechanical Engineering, Univ. Alaska, Fairbanks, USA

⁎ Corresponding author. Istituto Nazionale di GeofisCatania, Piazza Roma 2, 95123 Catania, Italy. Tel.: +39435801.

E-mail address: scollo@ct.ingv.it (S. Scollo).

0377-0273/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.jvolgeores.2010.12.004

a b s t r a c t

a r t i c l e i n f o

Article history:Received 2 July 2010Accepted 2 December 2010Available online 9 December 2010

Keywords:ash dispersalash forecasting and aviation safetyPUFF modelparametric study and model validationMt. Etna

In this paper we present a new statistical approach which provides tephra deposit load and ash concentrationusing PUFF, a Lagrangian model widely used to forecast volcanic ash dispersal during volcanic crisis. Weperform a parametric study in order to analyze the influence of each input parameter on model outputs. Forthis test, we simulate two eruptive scenarios similar to the 2001 (Scenario 1) and 1998 (Scenario 2) Etnaeruptions using high resolution weather data and a domain of 170×170 km. Results show that for bothscenarios, we are able to calculate the tephra deposit load and ash concentration but the use of millions ofparticles is required. Specifically, up to 33 and 220 millions of particles were necessary to accurately predictthe tephra deposit and ash concentration in air, respectively. This is approximately two orders of magnitudelarger than the values typically considered running PUFF. The parametric study shows that the horizontaldiffusion coefficient, the time step of the simulations, the topography and the standard deviation of theparticle distribution greatly affect the model outputs. We also validate the model by best-fit procedures.Results show a good comparison between field data of the 2001 Etna eruption and PUFF simulations, beinginside 5 and 1/5 times the observed data, comparable with results of Eulerian models.This work will allow to reliably outline the areas of contaminated airspace using PUFF or any other Lagrangianmodel in order to define the No Fly Zone and ensure the safety aviation operations as required after theEyjafjallajökull eruption.

ica e Vulcanologia, Sezione di095 7165861; fax: +39 095

l rights reserved.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Predictive models help significantly in reducing the risk associatedwith awide rangeof different volcanic activities (e.g. Keating et al., 2008).Simultaneously, sensitivity analysis techniques and uncertainty estima-tion are becoming more prevalent in order to study how the variation inmodel outputs can be attributed to different sources of variation inmodelinputs aswell as to estimate themodel reliability (e.g. Saltelli et al., 2008).For this aim, the use of data obtained by monitoring systems combinedwithmodeling strategies has become an important scientific goal inmostof the geophysical communities (Charpentier, 2008).

Volcanic ash released during explosive eruptions can be respon-sible for severe damage to aircraft, buildings, crops and telecommu-nications (e.g. Casadevall, 1994). As an example, during the recentEtna eruptions (e.g. 2001 and 2002–2003 activities) tephra falloutdrastically affected the local economy and transport system (e.g.Barnard, 2004). The mitigation of damage may be assisted by volcanicash transport and dispersion models (VATDM) that are able to

forecast the regions which will be affected by volcanic ash dispersaland fallout. However, it is clear that these models need to becompared with field data in order to estimate the model reliability.

The Istituto Nazionale di Geofisica e Vulcanologia, sezione diCatania (INGV-CT) runs four different tephra dispersal models daily:FALL3D (Costa et al., 2006), HAZMAP (Macedonio et al., 2005),TEPHRA (Bonadonna et al., 2005a), and PUFF (Searcy et al., 1998). Themodel forecasts are provided every day to the Italian civil protectionthat prepares for and manages emergencies (Scollo et al., 2009). Sofar, a parametric study and model validation analysis have only beencarried out at Etna for FALL3D (Costa et al., 2006), HAZMAP (Scolloet al., 2007), and TEPHRA (Scollo et al., 2006) by comparing modelresults with field data from the 2001 Etna eruption. TEPHRA was alsovalidated using data of the 1998 Etna and the 1996 Ruapehu eruptions(Scollo et al., 2008a). The PUFF model has not yet been validated in asimilar way.

PUFF is a volcanic ash tracking model initially developed tosimulate the movement of volcanic particles through a Lagrangianformulation of advection, fallout and turbulent diffusion based on arandom-walk technique. PUFF simulates the paths of N particles andprovides forecasts of the location of a given particle size at a specifictime instant. In order to compare PUFF simulations with field data, theevaluation of tephra ground accumulation and of ash concentration in

Table 1Volcanological input parameters of Scenario 1 (S1) and Scenario 2 (S2).

Scenario 1 (S1) Scenario 2 (S2)

Eruption duration 3 h 5 minAveraged mass flow rate (kg/s) 5×104 1×106

Plume height (km) 4.5 11Duration of simulation 3 h 3 h

Table 2Input parameters of the PUFF model.

Inputparameters

N Number of particles released by PUFF in each simulationashLogMean Base-10 log of the mean particle size (m)ashLogSdev Standard deviation of the particle size distribution (m)plumeMax Maximum plume height (m)plumeHwidth Initial horizontal width of the cloud (km)plumeShape Vertical distribution of particles within the initial eruption

column. It can be a linear, poissonian or exponential distributionplumeZwidth Initial vertical depth of the cloud (km) within which the ash

particles are initially distributeddiffuseZ Vertical diffusion coefficient (m2/s)diffuseH Horizontal diffusion coefficient (m2/s)dtMins Time step in the Lagrangian time-stepping method (min)Sedimentation Settling law which may be a constant laminar sedimentation

(Constant), pressure and temperature dependent air viscosity withlaminar sedimentation (Stokes) and a variable flow regimedependent on the particle Reynolds's number (Reynolds)

Topography Digital elevation model (DEM)

130 S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

air simulated by this code are needed. However, these quantitativeoutputs are not directly available from PUFF forecasts. An earlyattempt to make a straight-forward comparison between PUFFforecasts and field data was carried out by Tanaka and Yamamoto(2002) who drew a contour surrounding the ash deposit and countedthe mass of particles that fell over a unit area. However, this type ofcomputation has a certain degree of uncertainty. In fact, due to therandom processes used in PUFF, one could find a different number ofparticles in a fixed area and/or volume even if the model runs wereperformed with the “same” input parameters. Therefore, there is animportant issue which should first be addressed: if we run twosimulations using the same input parameters and then we calculatethe deposit and/or ash concentration maps, how large are thedifferences between two simulations?

In this workwe follow the Tanaka and Yamamoto (2002) approachand demonstrate that it is possible to reliably estimate the mass overan area or volume unit using the PUFF model. We apply a statisticalmethod to analyze PUFF simulations and evaluate the minimumnumber of particles (Nm) required for minimizing the differencesbetween two simulations when the same input parameters are used.

In order to apply the proposed method it is necessary to perform alarge number of simulations using a reasonable amount of computingtime. However, this is easily addressed thanks to the growth inperformance and capacity of microprocessors and the advancement inparallel computing techniques. In fact, parallel computer codes areincreasingly being used in Volcanology because they allow simulatingthe complex physical processes in a brief period of time during anongoing eruption (for example in 3D pyroclastic flows (e.g. Cavazzoniet al., 2005), and volcanic ash dispersal (e.g. Folch et al., 2008)). In thiswork a parallelization technique is applied for the first time to PUFFmodel in order to reduce the time computing.

The goal of this paper is threefold: the first goal is to investigate theability of PUFF to calculate the deposit load and ash concentration; thesecond and third goals are to perform a parametric study of inputparameters, and the evaluation of the reliability of PUFF outputsthrough comparisons with field data of a well-studied eruption.

The paper is structured as follows: Section 2 describes the methodused to calculate the deposit load and ash concentration, to performthe parametric study and model validation; results are presented inSection 3, and a discussion and concluding remarks are in Sections 4and 5, respectively.

2. The method

2.1. The eruptive scenarios

In our test, we consider two different eruptive scenarios which aresimulated daily at INGV-CT to forecast tephra dispersal from Etnavolcano (Scollo et al., 2009). These scenarios represent two differenttypologies of Etna explosive activity which were observed during thelast twenty years. The first scenario is similar to the first phase of 2001Etna eruption. During this phase the eruption column rose up to5 km a.s.l. producing a weak and bent over plume continuously for4 days (Scollo et al., 2007). The second scenario is similar to theexplosive event that occurred at Voragine crater on 22 July 1998. Theactivity produced a strong plume rising about 12 km a.s.l. (Andronicoet al., 1999) and represented one of the most powerful episodesobserved in the last ten years. The main features of the explosiveactivity were obtained by the analysis of field data for both the 2001(hereafter Scenario 1) and 1998 (hereafter Scenario 2) events, and theinput parameters necessary to simulate the dispersal by VATDM(Table 1) were identified for both events (Scollo et al., 2009).

We used Scenario 1 and Scenario 2 to perform the followingparametric study to PUFF model. Scenario 1 was also used to apply amodel validation technique. In fact, field data of the 2001 Etnaeruption (Scollo et al., 2007) has been widely used to validate several

volcanic ash transport and dispersion models (FALL3D, HAZMAP,VOL-CALPUFF, TEPHRA) and data are freely available for modelvalidation (http://www.ct.ingv.it/Progetti/Iavcei/index.htm).

2.2. The PUFF model

PUFF simulates the transport, dispersion and sedimentation ofvolcanic ash by evaluating at any time the position of thousands ofparticles. The model was initially developed by Tanaka (1994) andSearcy et al. (1998) with the aim of reducing the risk to aviation fromvolcanic ash encounters in the northwestern Pacific area. It has beenoperative at the Alaska Volcano Observatory since the eruption ofRedoubt volcano in 1989. The original code together with the mostrecent versions are freely available at the web-site http://www.puff.images.alaska.edu/downloads.shtml. PUFF forecasts have alreadybeen compared with many eruptions from Alaskan and Japanesevolcanoes (e.g. Tanaka and Yamamoto, 2002) and used to reproducethe dispersal of volcanic ash from theMay 18, 1980 eruption of MountSt. Helens (Fero et al., 2008), the 2001 eruption ofMt. Cleveland (Deanet al., 2004), the eruption of the Crater Peak vent, Mount Spurr, Alaskain August 1992 (Webley et al., 2009), the 1991 eruption of Mt.Pinatubo (Fero et al., 2009), and the 1991 eruption of Mt. Hudson(Kratzmann et al., 2010). For Etna volcano, Aloisi et al. (2002)simulated the dispersal of the paroxysm that occurred on 22 July 1998and Daniele et al. (2009) evaluated the area around the volcanoaffected by the presence of volcanic ash during the same event. PUFF istherefore widely used by a large scientific community and has alsobeen operative at INGV-CT since 2006 in order to forecast volcanic ashdispersal during Etna explosive eruptions (Scollo et al., 2009).

In this work, numerical simulations were carried out using PUFFversion 2.6. A detailed description of the model can be found in Searcyet al. (1998). Table 2 shows input parameters for PUFF used in ouranalysis (the italicized terms correspond with the option namewithinthe PUFF code).

Meteorological data are provided by the Italian Air ForceMeteorological Office and cover the entire area of Sicily from 12.5°

131S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

to 18.5° E and from 34.5° to 40.5° N. We use a form of codeparallelization known as “data parallelism” in which data aredistributed across different parallel computing nodes. In our method,PUFF runs on a cluster composed of 48 nodes and each node producesa number of outputs using a fixed number of volcanic particles.Results of the different simulations are subsequently summed in orderto obtain a simulation having a greater number of particles. It isnotable that this approach is possible because in the PUFFmodel thereare no interactions between the particles.

2.3. Computation of the tephra deposit and ash concentration

Consider the path of “one” particle computed by PUFF from theeruption column up to the time of deposition on the ground. After atime t the particle will fall onto the location (x1, y1) which is a functionof several randomly determined variables (e.g. the initial position ofthe particle inside the eruption column, the particle size that is afunction of the initial grain-size distribution, the random walk due tothe turbulence, wind speed and direction). Most variables depend onprobabilistic functions, and consequently if we repeat the simulationwithout any alteration, the new particle location will likely be (x2,y2)≠(x1, y1). It is therefore meaningful to pose the question: in agiven square (or volume) unit, what is the probability that the particlewill fall inside this specified surface (or volume)?

The answer to this question requires the use of a statistical approach.Hereafter we describe the approach for evaluating the mass on a givensurface S (thedeposit load). Similarly the sameapproachmaybe appliedto evaluate the mass in a given volume V (ash concentration).

If N represents the number of particles simulated by PUFF, and Psthe probability of finding a particle inside the surface unit S, forN largeenough, the number of particles Ns in S is given by N×Ps. In oursimulations, particles have different sizes. If c represents the sizeclasses, Nc the number of particles of size class c, and Pc the probabilityof finding the particle of size class c in S, the total number Ns of

particles in S is given by NS = ∑c

iNiPi. We are similarly able to

evaluate the total mass falling in S by MS = ∑c

imiNiPi, where mi is

the mass of particles estimated by the radius of the particles. In PUFF,all particles are, in fact, assumed spherical with the same density(2500 kg/m3). Keeping the same initial grain-size distribution of theparticles, for a large enough value of N, there is a linearity between Nand Ns (N∝Ns), and therefore also proportionality between the totalerupted mass M and Ms (M∝Ms). Similarly, we can write MES∝MS

ES

where ES is for a particular “eruptive scenario” (in our case MES is thetotal mass erupted in Scenario 1 or Scenario 2). Consequently, it ispossible to evaluate the mass in S (the deposit load) of the realeruptive scenario using MES

S = MES

M ⋅MS = γ⋅MS.In our study, we run PUFF using a high number of particle size and

perform the calculation following these steps: (1) define the surface S(volume V) having a size of 1 km×1 km (1 km×1 km×1 km); (2)calculate the total mass inside the surface (Ms) or volume (MV); and(3) scale this value by the factor γ obtaining the mass on surface S (orvolume V) for a given eruptive scenario MS

ES(MVES).

The main problem is: what is the minimum number of particles(Nm) so that this statistical approach is accurate? The basic premise isthat we need to increaseN until the ash concentration in S is very nearto the value obtained with a different simulation also using the samenumber N of particles.

Next the statistical approach used to find Nm is described. First, werun r simulations, each with Nini (the number of particles released byPUFF in each simulation). In our case Nini is equal to 50,000.Consequently, r outputs will be generated, each containing Nini

particles. These simulations are then taken randomly and summedin order to obtain an output composed of Ni= i⋅Nini particles with iranging between 1 and any integer positive value. For each Ni, we

generate a number of simulations n (again taking the previousoutputs randomly) and calculate the deposit load (ash concentration).Considering all the possible pairs of the deposit load (ash concentra-tion) generated using n simulations, we evaluate the correlationcoefficient ρp, qi (relative to the pair (p, q) and number of particles Ni)that is a measure of the relative stability of the result:

ρip;q =cov Rp;Rq

� �

σpσq=

E Rp−μp� �

Rq−μq� �n o

σpσq; ð1Þ

where R is the vectorized map concentration (the column vectorobtained using the vectorization of the matrix of ash concentration)and μ and σ are respectively the mean value and the standarddeviation of the vector R. If the simulations are similar, the value ofρp, qi approaches to 1. Furthermore, the mean value and standard

deviation of ρp, qi is evaluated for each Ni. For simplicity, we maymake a new vectorization of the matrix having elements ρp,qi obtaininga vector with elements ρji (with j=1.. ni(ni−1)/2).

As an example, suppose that we run r=8 simulations withNini=50,000 labeled as: a, b, c, d, e, f, g, and h. If the maximum value ofi is fixed to 5, Ni could vary between 50,000 and 250,000 (50,000×5).Consider N3=150,000 (that is generated by summing 3 runsrandomly), wemay choose to generate n=4 simulations by summing3 runs randomly, for example: A=[a b f]; B=[c d a], C=[d e h]; D=[a e g]. Now, the correlation coefficient ρj3 may be evaluated taking allthe combinations (AB, AC, AD, BC, BD, CD) obtaining 4×(4−1)/2=6correlation values. Finally, we evaluate the mean value and thestandard deviation using these six values of ρj3. This approach is thenrepeated for each value of Ni. In our analysis, we ran r=200simulations fixing Nini=50,000 in each separate run. These simula-tions are taken randomly and summed in order to obtain values of Ni

ranging between 50,000 and 7,500,000 with step of 50,000. For eachvalue ofNi, we generate n=20 simulations so that we have 190 valuesof ρji ((20×(20−1))/2). Furthermore, we calculate the mean value(μi) and the standard deviation (σi) of ρji (with respect to j). Using 190values of ρji, the mean value of ρji for each Ni is approximated using thefunction: ρji=Ni/(Ni+a). The minimum number of particles (Nm) isthen estimated to reach the stability of the final result. In our study,this is obtained when ρji=90%, 95% and 99%. Further, using Nm, thedeposit load (ash concentration) is evaluated.

It should be noted that the choice of a cell with side of 1 km wasmainly related to reach high resolution simulations. However, ourresults may be extended to a coarser mesh using the “ParzenWindows” approach (Duda et al., 2001). Following this approach,the surface S (volume V) changes with the number of particles as1=

ffiffiffiffiffiffiffiNm

p. Hence, if we use a cell with side of 5 km maintaining the

same domain (170 km×170 km), the Nm necessary to reach the samestability will be Nm/625 (Nm/15625 for the volume).

2.4. Parametric study and model validation

We performed a parametric study of input parameters in order toevaluate the difference between the two simulations of the tephradeposit due to the variation of each input parameter for Scenario 1 (S1)and Scenario 2 (S2).We changed input parameters of S1 (Table 3) and S2(Table 4) and for each sample of inputs, we calculateNm and the depositload (ash concentration). Given two simulations with vectorized mapconcentration Ri and Rj, their difference is quantified using:

Ji;j =1W ∑ Ri−Rj

� �2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1W ∑R2

i ⋅ 1W ∑R2

j

q ; ð2Þ

whereW is the number of grid points in the mesh or the length of thevectors Ri and Rj.

Table 3RUN of input parameters considered in the parametric study for Scenario 1 (S1). S1-RUN0 is the reference run. Input parameters are changed “one at time”with respect to S1-RUN0.

S1-RUN ashLogMean ashLogSdev plumeMax plumeHwidth plumeShape plumeZwidth diffuseZ diffuseH dtMins Sedimentation Topography

S1-RUN0 −3.6 (2 ϕ) 0.45 4500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN1-1 −3 (0 ϕ) 0.45 4500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN1-2 −3.3 (1 ϕ) 0.45 4500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN1-3 −3.9 (3 ϕ) 0.45 4500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN1-4 −4.2 (4 ϕ) 0.45 4500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN2-1 −3.6 0.3 4500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN2-2 −3.6 0.6 4500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN2-3 −3.6 1 4500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN2-4 −3.6 2 4500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN3-1 −3.6 0.45 3500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN3-2 −3.6 0.45 5500 0.001 Linear 1 10 10000 1 Reynolds DEMS1-RUN4-1 −3.6 0.45 500 0.01 Linear 1 10 10000 1 Reynolds DEMS1-RUN4-2 −3.6 0.45 500 0.1 Linear 1 10 10000 1 Reynolds DEMS1-RUN4-3 −3.6 0.45 500 1 Linear 1 10 10000 1 Reynolds DEMS1-RUN4-4 −3.6 0.45 500 10 Linear 1 10 10000 1 Reynolds DEMS1-RUN5-1 −3.6 0.45 500 0.001 Exponential 1 10 10000 1 Reynolds DEMS1-RUN5-2 −3.6 0.45 500 0.001 Poisson 1 10 10000 1 Reynolds DEMS1-RUN6-1 −3.6 0.45 500 0.001 Poisson 0.001 10 10000 1 Reynolds DEMS1-RUN6-2 −3.6 0.45 500 0.001 Poisson 0.0 10 10000 1 Reynolds DEMS1-RUN6-3 −3.6 0.45 500 0.001 Poisson 0.1 10 10000 1 Reynolds DEMS1-RUN7-1 −3.6 0.45 500 0.01 Linear 1 0.001 10000 1 Reynolds DEMS1-RUN7-2 −3.6 0.45 500 0.01 Linear 1 0.01 10000 1 Reynolds DEMS1-RUN7-3 −3.6 0.45 500 0.01 Linear 1 0.1 10000 1 Reynolds DEMS1-RUN7-4 −3.6 0.45 500 0.01 Linear 1 1 10000 1 Reynolds DEMS1-RUN7-5 −3.6 0.45 500 0.01 Linear 1 100 10000 1 Reynolds DEMS1-RUN8-1 −3.6 0.45 500 0.01 Linear 1 10 10 1 Reynolds DEMS1-RUN8-2 −3.6 0.45 500 0.01 Linear 1 10 100 1 Reynolds DEMS1-RUN8-3 −3.6 0.45 500 0.01 Linear 1 10 1000 1 Reynolds DEMS1-RUN8-4 −3.6 0.45 500 0.01 Linear 1 10 Turbulent 1 Reynolds DEMS1-RUN9-1 −3.6 0.45 500 0.01 Linear 1 10 10000 5 Reynolds DEMS1-RUN9-2 −3.6 0.45 500 0.01 Linear 1 10 10000 10 Reynolds DEMS1-RUN10-1 −3.6 0.45 500 0.01 Linear 1 10 10000 1 Constant DEMS1-RUN10-2 −3.6 0.45 500 0.01 Linear 1 10 10000 1 Stokes DEMS1-RUN11-1 −3.6 0.45 500 0.01 Linear 1 10 10000 1 Reynolds No DEM

Table 4RUN of input parameters considered in the parametric study for Scenario 2 (S2). S2-RUN0 is the reference run. Input parameters are changed “one at time”with respect to S2-RUN0.

S2-RUN ashLogMean ashLogSdev plumeMax plumeHwidth plumeShape plumeZwidth diffuseZ diffuseH dtMins Sedimentation Topography

S2-RUN0 −3.15 (0 ϕ) 0.45 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN1-1 −2.7 (−1 ϕ) 0.45 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN1-2 −2.3 (−2 ϕ) 0.45 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN1-3 −3.3 (1 ϕ) 0.45 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN1-4 −3.6 (2 ϕ) 0.45 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN1-5 −3.9 (3 ϕ) 0.45 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN1-6 −4.2 (4 ϕ) 0.45 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN2-1 −3.15 0.3 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN2-2 −3.15 0.6 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN2-3 −3.15 1 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN2-4 −3.15 2 11000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN3-1 −3.15 0.45 10000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN3-2 −3.15 0.45 12000 0.001 Linear 1 10 10000 1 Reynolds DEMS2-RUN4-1 −3.15 0.45 11000 0.01 Linear 1 10 10000 1 Reynolds DEMS2-RUN4-2 −3.15 0.45 11000 0.1 Linear 1 10 10000 1 Reynolds DEMS2-RUN4-3 −3.15 0.45 11000 1 Linear 1 10 10000 1 Reynolds DEMS2-RUN4-4 −3.15 0.45 11000 10 Linear 1 10 10000 1 Reynolds DEMS2-RUN5-1 −3.15 0.45 11000 0.001 Exponential 1 10 10000 1 Reynolds DEMS2-RUN5-2 −3.15 0.45 11000 0.001 Poisson 1 10 10000 1 Reynolds DEMS2-RUN6-1 −3.15 0.45 11000 0.001 Poisson 0.001 10 10000 1 Reynolds DEMS2-RUN6-2 −3.15 0.45 11000 0.001 Poisson 0.01 10 10000 1 Reynolds DEMS2-RUN6-3 −3.15 0.45 11000 0.001 Poisson 0.1 10 10000 1 Reynolds DEMS2-RUN7-1 −3.15 0.45 11000 0.01 Linear 1 0.001 10000 1 Reynolds DEMS2-RUN7-2 −3.15 0.45 11000 0.01 Linear 1 0.01 10000 1 Reynolds DEMS2-RUN7-3 −3.15 0.45 11000 0.01 Linear 1 0.1 10000 1 Reynolds DEMS2-RUN7-4 −3.15 0.45 11000 0.01 Linear 1 1 10000 1 Reynolds DEMS2-RUN7-5 −3.15 0.45 11000 0.01 Linear 1 100 10000 1 Reynolds DEMS2-RUN8-1 −3.15 0.45 11000 0.01 Linear 1 10 10 1 Reynolds DEMS2-RUN8-2 −3.15 0.45 11000 0.01 Linear 1 10 100 1 Reynolds DEMS2-RUN8-3 −3.15 0.45 11000 0.01 Linear 1 10 1000 1 Reynolds DEMS2-RUN8-4 −3.15 0.45 11000 0.01 Linear 1 10 Turbulent 1 Reynolds DEMS2-RUN9-1 −3.15 0.45 11000 0.01 Linear 1 10 10000 5 Reynolds DEMS2-RUN9-2 −3.15 0.45 11000 0.01 Linear 1 10 10000 10 Reynolds DEMS2-RUN10-1 −3.15 0.45 11000 0.01 Linear 1 10 10000 1 Constant DEMS2-RUN10-2 −3.15 0.45 11000 0.01 Linear 1 10 10000 1 Stokes DEMS2-RUN11-1 −3.15 0.45 11000 0.01 Linear 1 10 10000 1 Reynolds No DEM

132 S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

Fig. 2. Correlation coefficient (ρji) in function of the number of particles (Ni) for Scenario1. The yellow circle shows the number of particles necessary to reach the 99% of ρji onthe ground. The mean value (μi) and the standard deviation (σi) of ρji are plotted usingthe black and broken blue line, respectively. The red line represents themean value of ρji

evaluated by ρji=Ni/(Ni+a). (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

133S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

When Ji,j is near 0 the runs are similar, and consequently thevariation due to a specific input parameter does not significantly affectthe result. Following the approach of Scollo et al. (2009), we classifythe difference between two runs as low if Δ≤0.33, moderate if0.33bΔ≤0.66, high if 0.66bΔ≤0.99 and extreme if Δ≥1.

Model validation was carried out in order to find input parametersof the PUFF model that fit better the 2001 field data. The completedescription of the eruption and analysis of the field data can be foundin Scollo et al. (2007). Input parameters were changed following thesame table used for the previous parametric study of S1 (Table 3) andthe simulation results were compared with field data by a standardbest fit function (e.g. Bonadonna et al., 2002).

3. Results

3.1. Tephra deposit load and ash concentration computation

For each scenario, we evaluate the values of Nm required to reach90%, 95% and 99% of ρji on the ground and at 1828 m (FL60, where FLindicates the flight level), at 3657 m (FL120) and at 5486 m (FL180)above sea level. Fig. 1 shows the number of particles Nm requiredto reach 99% of ρji for S1 and using input parameters as describedin Table 3. It is notable that if the value of dtMins is equal to 5 or 10(S1-RUN9-1, S1-RUN9-2), a great number of particles are necessaryto reach convergence. Setting this parameter to 1 improves theLagrangian method, so we recommend that large values of dtMinsshould be avoided. Furthermore, high value of Nm occurredincreasing the values of the standard deviation of the total grain-size distribution (S1-RUN2-3, S1-RUN2-4) and excluding the topog-raphy (S1-RUN11-1).

In particular, we found that for S1-RUN0, 99% of ρji is reached onthe ground using only 5.2 M (million) of particles (Fig. 2). However, agreater number of particles are needed for FL60, FL120 and FL180levels being about 130 M, 56 M and 250 M respectively (Fig. 1). It isnotable also that a large number of particles are required at FL180probably because only a small number of the total particles reach thisupper elevation.

Scenario 2 has similar features to Scenario 1. Fig. 3 shows thenumber of particles Nm necessary to reach 99% of ρji for S2 using inputparameters as described in Table 4. Again, the standard deviation ofthe total grain-size distribution (S2-RUN2-3, S2-RUN2-4), the timestep (S2-RUN9-1, S2-RUN9-2) and the topography (S1-RUN11-1)

Fig. 1. Log of the minimum number of particles (Nm) required to reach the 99% of ρji o

affect the value of Nm. There is also an increase in Nm with an increasein the mean of the total grain-size distribution (S2-RUN1-1 and S2-RUN1-2).

Fig. 4 shows the ρji plot as a function of Ni for S2-RUN0 and thecomputation of ρji at 95% on the ground. It is obtained using about4.7 M particles, whereas 24 M particles are necessary to increase ρji to99% (Fig. 3).

Table 5 shows Nm (averaged over all runs from RUN0 to RUN11),for S1 and S2 on the ground and at FL60, FL120 and FL180. It is notablethat Nm increases with the increase of the correlation coefficient(ρji=99%). The convergence of 90% and 95% is reached with a numberof particles less than about 7 M on the ground and less than about45 M at different flight level for both scenarios. Furthermore, exceptfor the deposit load, S1 needs a greater number of particles to calculatethe ash concentration at different flight levels than S2 (about 5 timesmore). We note that the convergence is obtained easily in those

n the ground and at different flight levels (FL60, FL120, and FL180) for Scenario 1.

Fig. 3. Log of the minimum number of particles (Nm) required to reach the 99% of ρji on the ground and at different flight levels (FL60, FL120, and FL180) for Scenario 2.

134 S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

regions where a large number of particles are present and it is strictlylinked to input parameters used in the simulations.

Fig. 5 shows the comparison between the computed deposits using50,000 particles and 5.2 M particles for S1-RUN0 and Fig. 6 using50,000 and 4.6 M particles for S2-RUN0. Increasing the number ofparticles clearly causes a decrease in the noise and a stabilization ofdeposit load (ash concentration) maps.

Finally, it is highlighted that Nm may change with respect to theweather conditions. Simulations were carried out for S1-RUN0 usingthe forecasting weather data of 10 November 2007 between 3:00 and6:00AMand 6August 2007 between3:00 and6:00 AM, days thatwerecharacterized by high speed winds (75 and 98 knts at 3000 and5000 m) and near-zero wind, respectively. In these dramaticallydifferentweather conditions,we found a difference inNm of about 30%.

3.2. The parametric study

Table 6 shows the results of the parametric study for S1. It iscarried out changing the input parameters (Tables 3 and 4) and

Fig. 4. Correlation coefficient (ρji) in function of the number of particles (Ni) for Scenario2. Color lines as described in Fig. 2. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)

comparing the computed deposit between two simulations by Eq. (2).All these runs were carried out with the maximum number ofparticles (7.5 M particles). It is remarkable that extreme differencesoccur if we introduce the topography (DEM) and change the diffuseHand dtMins parameters.

Regarding the use of a DEM, it is notable that the top of Etna withits steep slopes and 3350 m a.s.l. elevation strongly affects the localwind circulation (Favalli et al., 2004). Results in Table 6 show thatPUFF is very sensitive to this parameter and similar results would beexpected for most other volcanoes having a complex orography likeEtna. The diffuseH parameter defines the horizontal diffusioncoefficient (m2/s) used in the random-walk method of diffusion.When the horizontal diffusion is near 0, the lateral spreading ofvolcanic clouds occurs only by wind advection. This parameter has animportant role on the volcanic ash dispersal and should be setaccurately.

The parameter dtMins controls the time step of the simulations.The default value is 10 min, but smaller value should be used in orderto obtain finer time results. Quantitatively, the previous analysis hasshown that the value should be set to 1 (Section 3.1). If not, thecomputational time required due to the necessary large value of Nm,could be unmanageable. Table 6 shows that the standard deviation ofthe particle distribution also has an important effect on the finalresults. The variation of the standard deviation modifies the sizedistribution of volcanic particles and consequently the terminalsettling velocity distribution. The particle velocity can follow differentlaws: (1) the Stokes law with a constant air viscosity (“Constant”option); (2) the Stokes law in which the effect of pressure andtemperature on air viscosity is accounted for (“Stokes” option); (3) anempirical function of the particle Reynold's number (“Reynolds”

Table 5Minimum number of particles Nm in millions averaged over all runs from RUN0 toRUN11 for Scenario 1 (S1) and Scenario 2 (S2) on the ground (G) and at FL60, FL120 andFL180.

G FL60 FL120 FL180

S1-90% 0.6 13.9 6.9 19.9S1-95% 1.3 29.5 14.6 41.9S1-99% 7.3 153.5 76.1 219.8S2-90% 2.9 2.3 1.7 2.6S2-95% 6.2 5.1 3.7 5.5S2-99% 32.5 26.1 19.2 28.9

Fig. 5. Comparison between the computed deposits using 50,000 particles (top) and 5.2 M of particles for S1-RUN0 (bottom).

135S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

Fig. 6. Comparison between the computed deposits using 50,000 particles (top) and 4.7 M of particles for S2-RUN0 (bottom).

136 S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

Table 6Values of Ji,j for Scenario 1 (S1). Green color indicates low differences (Δ≤0.33), yellow moderate differences (0.33bΔ≤0.66), orange high differences (0.66bΔ≤0.99) and, finally, red extreme differences (Δ≥1).

S1

RUN

0

RUN

1-1

RUN

1-2

RUN

1-3

RUN

1-4

RUN

2-1

RUN

2-2

RUN

2-3

RUN

2-4

RUN

3-1

RUN

3-2

RUN

4-1

RUN

4-2

RUN

4-3

RUN

4-4

RUN

5-1

RUN

5-2

RUN

6-1

RUN

6-2

RUN

6-3

RUN

7-1

RUN

7-2

RUN

7-3

RUN

7-4

RUN

7-5

RUN

8-1

RUN

8-2

RUN

8-3

RUN

8-4

RUN

9-1

RUN

9-2

RUN

10-1

RUN

10-2

RUN

11-1

RUN0 0.00 0.10 0.04 0.07 0.26 0.39 0.21 0.28 0.34 0.20 0.14 0.02 0.03 0.03 0.15 0.10 0.03 0.57 0.62 0.48 0.03 0.03 0.02 0.02 0.02 2.12 1.78 0.90 1.48 8.61 3.11 0.27 0.28 1.38

0.002.033.79 4.81 3.86 1.16 1.380.01 0.00 2.630.41 0.75 13.40 5.420.00 0.01 2.570.46 0.82 13.22 5.355.35 5.42 1.167.59 9.57 1.60 0.00

13.22 13.40 3.8617.81 21.86 0.00 1.600.82 0.75 4.810.11 0.00 21.86 9.570.46 0.41 3.790.00 0.11 17.81 7.591.01 0.95 5.370.21 0.04 24.07 10.671.24 1.17 5.940.36 0.12 26.35 11.790.29 0.30 1.370.94 1.53 8.49 3.040.26 0.26 1.470.82 1.38 8.80 3.200.29 0.30 1.360.91 1.50 8.48 3.040.31 0.31 1.300.94 1.53 8.23 2.920.28 0.28 1.370.83 1.40 8.44 3.041.22 1.26 0.412.14 2.95 5.17 1.491.43 1.47 0.342.42 3.25 4.90 1.371.37 1.41 0.432.25 3.08 5.19 1.510.33 0.33 1.330.97 1.58 8.30 2.970.58 0.59 0.891.34 2.02 6.70 2.190.70 0.71 0.841.62 2.37 6.13 1.990.32 0.33 1.250.98 1.58 8.05 2.830.29 0.30 1.340.91 1.48 8.31 2.960.28 0.28 1.360.89 1.45 8.45 3.020.66 0.68 0.791.44 2.16 6.27 2.000.09 0.07 2.510.49 0.86 12.71 5.090.10 0.10 2.420.48 0.79 12.74 5.170.06 0.05 2.530.47 0.80 12.94 5.230.09 0.09 2.350.44 0.84 12.33 4.911.22 1.23 0.762.19 3.11 4.55 1.290.93 0.94 0.841.75 2.56 5.26 1.620.50 0.51 1.061.22 1.90 6.94 2.34

1.47 1.37 5.94 5.370.41 1.37 1.30 1.360.26 0.30 1.17 0.951.26 0.28 0.31 0.300.26 0.29 1.24 1.011.22 0.28 0.31 0.293.20 3.04 11.79 10.671.49 3.04 2.92 3.048.80 8.49 26.35 24.075.17 8.44 8.23 8.481.38 1.53 0.12 0.042.95 1.40 1.53 1.500.82 0.94 0.36 0.212.14 0.83 0.94 0.911.70 1.85 0.03 0.003.39 1.70 1.85 1.832.03 2.19 0.00 0.033.84 2.02 2.19 2.170.02 0.00 2.19 1.850.45 0.02 0.010.00 0.02 2.03 1.700.51 0.03

0.030.02

0.02 0.01 2.17 1.830.46 0.03 0.020.02

0.000.03 0.02 2.19 1.850.40 0.02 0.00 0.020.02 0.03 2.02 1.700.45 0.00 0.02 0.030.51 0.45 3.84 3.390.00 0.45 0.40 0.460.67 0.60 4.18 3.710.06 0.59 0.53 0.600.61 0.55 4.00 3.540.09 0.57 0.50 0.550.02 0.02 2.26 1.910.45 0.04 0.04 0.020.11 0.09 2.79 2.400.20 0.09 0.07 0.090.17 0.14 3.17 2.760.24 0.15 0.12 0.140.03 0.02 2.24 1.900.38 0.03 0.02 0.030.02 0.02 2.13 1.800.42 0.02 0.02 0.020.02 0.02 2.09 1.760.45 0.02 0.02 0.030.16 0.14 2.97 2.550.15 0.13 0.11 0.130.17 0.21 1.34 1.081.19 0.22 0.25 0.210.36 0.38 1.18 0.961.20 0.34 0.38 0.380.25 0.29 1.23 1.001.22 0.28 0.32 0.290.16 0.20 1.32 1.071.08 0.18 0.23 0.200.39 0.36 4.16 3.630.24 0.37 0.34 0.360.26 0.24 3.50 3.020.24 0.23 0.22 0.240.07 0.06 2.67 2.280.31 0.06 0.05 0.05

0.89 1.33 0.43 0.340.59 0.33 1.41 1.470.58 0.33 1.37 1.432.19 2.97 1.51 1.376.70 8.30 5.19 4.902.02 1.58 3.08 3.251.34 0.97 2.25 2.422.40 1.91 3.54 3.712.79 2.26 4.00 4.180.09 0.02 0.55 0.600.11 0.02 0.61 0.670.09 0.02 0.55 0.600.07 0.04 0.50 0.530.09 0.04 0.57 0.590.20 0.45 0.09 0.060.28 0.59 0.08 0.000.27 0.56 0.00 0.080.09 0.00 0.56 0.590.00 0.09 0.27 0.280.06 0.14 0.34 0.330.06 0.04 0.48 0.510.08 0.03 0.52 0.560.09 0.03 0.56 0.590.03 0.12 0.24 0.230.51 0.23 1.34 1.410.64 0.42 1.36 1.410.57 0.32 1.37 1.430.48 0.21 1.25 1.310.17 0.33 0.32 0.310.12 0.22 0.35 0.340.05 0.05 0.39 0.41

1.36 1.34 1.25 0.840.28 0.30 0.33 0.710.28 0.29 0.32 0.703.02 2.96 2.83 1.998.45 8.31 8.05 6.131.45 1.48 1.58 2.370.89 0.91 0.98 1.621.76 1.80 1.90 2.762.09 2.13 2.24 3.170.02 0.02 0.02 0.140.02 0.02 0.03 0.170.03 0.02 0.03 0.140.02 0.02 0.02 0.120.02 0.02 0.03 0.150.45 0.42 0.38 0.240.59 0.56 0.51 0.330.56 0.52 0.48 0.340.03 0.03 0.04 0.140.09 0.08 0.06 0.060.14 0.14 0.10 0.000.02 0.02 0.00 0.100.02 0.00 0.02 0.140.00 0.02 0.02 0.140.13 0.12 0.10 0.080.20 0.23 0.26 0.590.35 0.38 0.40 0.740.28 0.28 0.34 0.680.21 0.22 0.25 0.580.36 0.35 0.32 0.140.24 0.23 0.21 0.110.07 0.06 0.05 0.07

2.53 2.42 2.51 0.790.05 0.10 0.07 0.680.06 0.10 0.09 0.665.23 5.17 5.09 2.00

12.94 12.74 12.71 6.270.80 0.79 0.86 2.160.47 0.48 0.49 1.441.00 0.96 1.08 2.551.23 1.18 1.34 2.970.29 0.38 0.21 0.140.25 0.36 0.17 0.160.29 0.38 0.21 0.130.32 0.38 0.25 0.110.28 0.34 0.22 0.131.22 1.20 1.19 0.151.43 1.41 1.41 0.231.37 1.36 1.34 0.240.32 0.42 0.23 0.120.57 0.64 0.51 0.030.68 0.74 0.59 0.080.34 0.40 0.26 0.100.28 0.38 0.23 0.120.28 0.35 0.20 0.130.65 0.68 0.60 0.000.09 0.21 0.00 0.600.14 0.00 0.21 0.680.00 0.14 0.09 0.650.10 0.19 0.07 0.541.18 1.25 1.04 0.140.89 0.95 0.78 0.090.49 0.56 0.41 0.05

0.15 0.15 1.70

1.38 2.03 1.70 1.06 0.84 0.76 2.350.28 0.07 0.15 0.51 0.94 1.23 0.090.27 0.07 0.15 0.50 0.93 1.22 0.093.11 4.33 3.72 2.34 1.62 1.29 4.918.61 11.19 9.88 6.94 5.26 4.55 12.331.48 0.97 1.22 1.90 2.56 3.11 0.840.90 0.53 0.72 1.22 1.75 2.19 0.441.78 1.21 1.49 2.28 3.02 3.63 1.072.12 1.48 1.80 2.67 3.50 4.16 1.320.02 0.10 0.05 0.06 0.24 0.36 0.200.02 0.08 0.04 0.07 0.26 0.39 0.160.02 0.10 0.05 0.05 0.24 0.36 0.200.03 0.11 0.06 0.05 0.22 0.34 0.230.03 0.10 0.06 0.06 0.23 0.37 0.180.48 0.85 0.65 0.31 0.24 0.24 1.080.62 1.03 0.81 0.41 0.34 0.31 1.310.57 0.97 0.75 0.39 0.35 0.32 1.250.03 0.14 0.07 0.05 0.22 0.33 0.210.10 0.31 0.19 0.05 0.12 0.17 0.480.15 0.40 0.26 0.07 0.11 0.14 0.580.03 0.13 0.06 0.05 0.21 0.32 0.250.03 0.11 0.05 0.06 0.23 0.35 0.220.02 0.10 0.05 0.07 0.24 0.36 0.210.14 0.38 0.26 0.05 0.09 0.14 0.540.20 0.06 0.11 0.41 0.78 1.04 0.070.34 0.16 0.25 0.56 0.95 1.25 0.190.28 0.08 0.17 0.49 0.89 1.18 0.100.21 0.06 0.13 0.37 0.74 0.99 0.000.39 0.80 0.59 0.18 0.04 0.00 0.990.26 0.58 0.42 0.11 0.00 0.04 0.740.07 0.25 0.16 0.00 0.11 0.18 0.37

0.72 1.22 9.88 3.720.04 0.05 1.80 1.490.65 0.06 0.06 0.050.19 0.07 0.75 0.810.05 0.05 0.06 0.260.17 0.25 0.11 0.260.07 0.07 2.03

0.04 0.04 0.00 0.16 0.42 0.59 0.130.53 0.97 11.19 4.330.08 0.10 1.48 1.210.85 0.10 0.11 0.100.31 0.14 0.97 1.030.10 0.11 0.13 0.400.08 0.16 0.06 0.380.25 0.58 0.80 0.060.10 0.00RUN1-1 0.04

RUN1-2RUN1-3RUN1-4RUN2-1RUN2-2RUN2-3RUN2-4RUN3-1RUN3-2RUN4-1RUN4-2RUN4-3RUN4-4RUN5-1RUN5-2RUN6-1RUN6-2RUN6-3RUN7-1RUN7-2RUN7-3RUN7-4RUN7-5RUN8-1RUN8-2RUN8-3RUN8-4RUN9-1RUN9-2RUN10-1RUN10-2RUN11-1

137S.Scollo

etal./

Journalof

Volcanology

andGeotherm

alResearch

200(2011)

129–142

Table 7Values of Ji,j for Scenario 2 (S2). Green color indicates low differences (Δ≤0.33), yellow moderate differences (0.33bΔ≤0.66), orange high differences (0.66bΔ≤0.99) and, finally, red extreme differences (Δ≥1).

RUN

0

0.00

0.790.62

0.750.83

0.101.86

0.090.08

0.080.07

0.630.13

0.861.65

0.100.09

0.100.100.091.941.600.51

1.404.61

1.382.44

0.301.37

0.190.39

0.61

0.66

0.12

1.23

0.29

RUN

11-1

0.300.64

2.502.460.00

1.362.003.551.75

0.320.322.512.26

0.390.340.320.27

0.270.400.41

0.250.370.270.32

3.230.380.280.30

0.950.451.182.76

1.010.230.310.48

RUN

9-1

4.61

12.334.534.634.434.714.643.06

3.123.123.04

3.144.084.66

11.498.64

10.650.001.34

4.414.534.414.86

14.3412.61

7.772.461.902.463.31

11.6611.83

6.04

3.55

4.037.29

RUN

9-2

2.44

7.542.372.462.322.502.491.40

1.421.501.41

1.422.132.47

6.98

6.415.07

1.340.00

2.382.31

2.302.61

7.698.75

4.541.000.78

1.582.05

7.097.19

3.38

1.75

1.06

4.23

RUN

10-1

1.38

1.07

1.321.44

1.271.44

3.471.33

3.293.503.61

3.2 1.581.251.461.42

1.05

0.920.82

11.837.19

1.511.22

0.050.25

0.373.484.98

1.73

0.00

0.71

2.500.01

2.343.48

0.38

RUN

10-2

1.37

1.08

1.301.42

1.261.41

3.401.31

3.56

3.233.233.44

1.55

1.40

1.231.42

1.06

0.940.82

11.667.09

1.491.20

0.070.30

0.353.434.92

0.01

0.70

0.002.46

1.702.303.43

0.38

RUN

8-1

1.86

2.07

2.031.88

1.771.863.363.463.153.203.372.231.97

0.360.09

12.337.54

2.022.032.001.86

0.000.03

0.981.151.184.055.624.053.00

1.071.08

1.43

2.51

2.281.16

RUN

8-2

1.65

1.85

1.821.68

1.571.653.053.152.872.903.072.031.77

0.250.03

11.496.98

1.811.811.801.66

0.000.03

0.951.141.083.705.163.712.73

1.051.06

1.27

2.26

2.041.04

RUN

8-4

1.40

0.091.581.411.551.311.412.742.862.632.612.751.741.49

0.030.130.00

10.656.41

1.541.54

1.561.400.871.030.903.304.653.312.39

0.920.94

1.05

2.00

1.760.85

RUN

8-3

0.86

0.360.990.830.940.770.842.022.131.951.881.991.120.88

0.250.000.138.645.07

0.940.920.950.840.980.950.542.363.492.381.60

0.820.82

0.59

1.36

1.110.52

RUN

7-3

0.09

2.030.080.08

0.800.780.580.580.100.07

1.820.941.554.432.32

0.040.060.090.08

0.00

0.690.080.08

2.131.650.500.561.160.600.24

1.441.41

0.17

0.27

0.410.09

RUN

7-4

0.08

1.880.12

0.080.00

0.080.100.800.85

0.660.86

0.650.120.07

0.831.414.632.46

0.080.080.110.09

1.68

1.941.530.460.631.250.670.29

1.321.30

0.16

0.32

0.340.12

RUN

7-5

0.10

2.07

0.080.12

0.120.110.740.85

0.620.82

0.610.150.10

0.991.584.532.37

0.090.090.130.09

0.00

1.85

2.071.620.550.591.200.640.28

1.441.42

0.20

0.32

0.430.09

RUN

6-2

0.83

0.800.850.853.46

0.890.890.180.00

0.200.810.93

3.152.132.863.041.41

0.780.850.770.97

0.190.15

4.403.902.110.490.870.57

3.613.56

1.41

0.661.91

0.41

0.55

RUN

6-3

0.75

0.743.36

0.800.820.690.80

0.000.18

0.130.190.750.82

3.052.022.743.061.40

0.670.770.730.87

0.25

4.293.741.940.450.840.52

3.473.40

1.28

0.571.78

0.39

0.50

RUN

7-1

0.08

1.86

0.10

0.09

0.11

0.08

0.800.89

0.660.670.130.07

1.650.841.414.642.49

0.090.110.090.09

0.00

0.81

2.011.560.440.641.260.68

1.331.31

0.17

0.140.37

0.34

0.28

RUN

7-2

0.07

1.770.120.08

0.890.860.690.680.120.08

1.570.771.314.712.50

0.080.080.090.09

0.00

0.820.09

0.08

1.831.490.460.641.280.68

1.271.26

0.140.33

0.32

0.120.27

RUN

4-4

0.13

0.120.100.12

2.230.15

0.13

0.810.75

0.620.80

0.63

2.031.121.744.082.13

0.130.13

0.00

0.130.100.09

2.311.810.620.471.030.50

1.581.550.27

0.260.510.110.22

RUN

5-1

0.63

0.680.580.650.613.37

0.67

0.200.19

0.000.630.70

3.071.992.753.141.42

0.580.630.580.74

0.100.24

4.143.581.790.390.830.45

3.283.23

1.151.62

0.32

0.470.37

RUN

5-2

0.62

0.690.580.660.623.20

0.660.130.15

0.100.620.70

2.901.882.613.121.42

0.560.630.570.74

0.150.00

4.153.571.790.390.830.44

3.293.23

1.151.62

0.27

0.460.40

RUN

6-1

0.79

0.860.780.860.823.15

0.25

0.240.800.90

2.871.952.633.121.50

0.750.830.730.94

0.19

0.81

0.000.15

4.313.792.010.520.910.56

3.503.44

1.361.83

0.40

0.650.57

RUN

3-2

0.10

0.570.730.770.73

2.000.13

0.090.11

0.090.09

0.580.130.10

1.800.951.564.412.30

0.090.080.000.112.181.700.540.551.140.59

1.511.490.28

0.220.440.120.21

RUN

4-1

0.10

0.770.850.830.63

2.030.09

0.060.08

0.080.11

0.630.130.07

1.810.921.544.532.38

0.070.000.080.092.091.600.480.591.200.63

1.421.400.30

0.170.400.100.26

RUN

4-2

0.10

0.560.750.780.67

2.02

0.09

0.090.080.040.08

0.580.100.07

1.810.941.544.412.31

0.00

0.090.08

0.07

2.151.670.510.551.170.59

1.461.420.25

0.180.410.080.22

RUN

4-3

0.09

0.07

0.080.07

0.07

1.970.10

0.930.82

0.700.90

0.700.09

1.770.881.494.662.47

0.100.06

0.00

0.070.07

1.921.450.400.611.240.65

1.251.230.37

0.140.340.110.26

RUN

2-2

0.51

0.440.46

2.111.94

1.792.01

0.50

0.550.46

1.18

1.790.620.40

1.080.540.907.774.54

0.510.480.540.390.860.490.001.872.891.89

0.370.351.18

0.150.090.701.11

RUN

2-3

1.60

1.491.56

3.903.74

3.573.79

1.651.531.621.15

3.581.811.45

1.140.951.03

12.617.69

1.671.601.701.390.260.000.493.815.403.81

0.050.072.76

0.860.501.942.62

RUN

2-4

1.94

2.011.83

4.404.29

4.154.31

0.982.071.942.13

4.142.311.92

0.950.980.87

14.338.75

2.152.09

0.001.812.18

0.260.864.536.294.59

0.250.303.23

1.230.782.433.24

RUN

3-1

0.09

0.870.970.940.74

1.860.09

0.080.09

0.090.09

0.740.130.06

1.660.841.404.862.61

0.080.09

1.810.000.11

1.390.390.681.360.73

1.221.200.38

0.120.330.120.32

RUN

1-4

0.29

0.280.270.24

0.500.550.570.40

0.29

3.000.28

0.370.220.26

2.731.602.393.311.58

0.220.260.210.323.242.621.110.200.640.24

2.232.300.31

0.600.960.170.00

RUN

1-5

0.66

0.520.570.560.44

0.680.60

0.68

0.670.644.05

0.450.500.65

3.712.383.312.461.06

0.590.630.590.734.593.811.890.080.310.00

3.483.430.48

1.201.700.440.24

RUN

1-6

1.23

0.840.870.910.83

1.261.28

1.251.16

1.205.62

0.831.031.24

5.163.494.651.900.78

1.171.201.141.366.295.402.890.240.000.31

4.984.920.95

1.992.640.970.64

RUN

2-1

0.61

0.450.490.520.39

0.640.64

0.630.56

0.594.05

0.390.470.61

3.702.363.302.461.00

0.550.590.550.684.533.811.870.000.240.08

3.483.430.45

1.171.680.410.20

RUN

1-3

0.12

2.280.090.12

0.140.120.09

0.570.660.650.460.470.110.11

2.041.111.764.032.05

0.08

0.120.10

0.122.431.940.690.41

1.721.700.23

0.300.590.00

0.440.97

0.17

RUN

1-1

0.19

1.361.15

1.281.41

0.201.43

0.170.16

0.170.14

1.150.26

1.270.59

0.180.14

0.220.17

0.121.230.860.15

1.056.04

0.713.38

0.700.64

0.000.09

1.17

1.201.99

0.600.30

RUN

1-2

0.39

1.831.62

1.781.91

0.37

1.160.430.340.410.33

1.620.51

1.040.52

0.410.34

0.440.40

0.330.780.500.09

0.85

4.237.29

0.380.381.01

0.090.00

1.68

1.702.64

0.960.59

S2

RUN0RUN1 -1RUN1-2RUN1-3RUN1-4RUN1-5RUN1-6RUN2-1RUN2-2RUN2-3RUN2-4RUN3-1RUN3-2RUN4-1RUN4-2RUN4-3RUN4-4RUN5-1RUN5-2RUN6-1RUN6-2RUN6-3RUN7-1RUN7-2RUN7-3RUN7-4RUN7-5RUN8-1RUN8-2RUN8-3

RUN10-2RUN11-1

RUN8-4RUN9-1RUN9-2RUN10-1

138S.Scollo

etal./

Journalof

Volcanology

andGeotherm

alResearch

200(2011)

129–142

Fig. 7. Comparison between the simulation using the values obtained by the best-fitprocedure and the field data at each sampling point (kg m−2) of the 2001 Etna eruption(Scollo et al., 2007). The equiline represents an ideal line if a perfect agreement exists,the dotted lines marks the region between 5 and 1/5 times the observed mass at eachstation.

139S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

option) as suggested in Bonadonna et al. (1998). As expected, thesevariations cause extreme differences in the forecasted deposit becauseterminal settling velocity has an important effect on sedimentationprocesses (e.g. Pfeiffer et al., 2005). This conclusion is also confirmedby increasing the percentage of fine particles in the total grain-sizedistribution, which results in large differences as seen in Table 6.

Table 7 shows the results for S2. Both the diffuseH and dtMinsparameters have important effects on the computed dispersal anddeposit. The use of the DEM has instead a secondary effect. This isexpected for eruption columns which have heights of severalkilometers due to the fact that volcanic particles have to travel alonger distance from the initial volcanic plume to the ground in S2. Forthe same reason, the model of the terminal settling velocity has amajor influence and consequently should be as accurate as possible. Itis notable that while errors up to 2 ϕ (ϕ is for −log2d, where d is thediameter in mm) for ashLogMean parameter are low or moderate(Table 7) the ashLogSdev parameter has a major effect on the deposit.Furthermore, the plumeShape parameter describing the initialdistribution of particles inside the column may play an importanteffect on the deposition for this scenario.

For both scenarios, the effect of the variation in the verticaldiffusion coefficient is relatively irrelevant. The parameter was variedbetween 0.001 and 100 but substantial differences with RUN0 werenot observed. We also found that the model is not sensitive toplumeHwidth, indicating that the ash plume is advected in a verysimilar manner within the same grid cell. Instead, plumeZwidth (theinitial vertical depth of the cloud) may more substantially affect thepattern deposition for both scenarios. This is in agreement withWebley et al. (2009) who found that the accuracy of the verticaldistribution is important in the initial source condition.

3.3. Model validation

We perform a best-fit procedure in order to find the inputparameters of PUFF which give a better agreement with the field dataof the 2001 Etna eruption (Scollo et al., 2007). Input parameters weremodified following Table 3, and for each run we calculate the depositand perform the best fit procedure. Results are shown in Table 8. Wefound the optimal ashLogMean parameter is equal to −3.9(0.125 mm/3 ϕ) and ashLogSdev equal to 0.3 (0.5 mm/1 ϕ), implyingfiner grain-size than Scollo et al. (2007). An initial column height of5500 m gives the best fit in agreement with observations carried outby MISR (Scollo et al., 2010). The best fit for the initial particledistribution is a linear distribution. Similarly, for the same eruption,the results of the HAZMAP model show the maximum concentrationof the total mass located at the middle of the eruption column and notconcentrated around the maximum (Scollo et al., 2007).

It is notable that the best description of the sedimentation isobtained using the “Reynold's settling law”. At the moment it is thebest settling description available in PUFF as it accounts for the mostof the complex dynamics of volcanic ash fallout. Further, the time stepis set to 1 min and the use of an accurate DEMgives the best results (aswe expected for an eruption producing a weak plume). Fig. 7 shows

Table 8PUFF input parameters that best fit the field data of the 2001 Etna eruption.

ashLogMean −3.9ashLogSdev 0.3plumeMax 5500plumeShape linearplumeZwidth 0.1plumeHwidth 0.01diffuseZ 1diffuseH 1000Sedimentation ReynoldsdtMins 1DEM gtopo30

the comparison between the PUFF simulation using the best fit valuesand the field data of the 2001 explosive event. Results show that allpoints are inside 5 and 1/5 times the observed data. These results arehence comparable with those obtained by other tephra dispersalmodels like HAZMAP and FALL3D (see Scollo et al., 2008b).

4. Discussion

4.1. The number of particles

In this analysis, we tested the ability of PUFF to compute thedeposit load and ash concentration. Using two standard scenarios forthe eruptive behavior of Etna, we found that the ash concentration canbe computed using millions of particles. Consequently, we are nowable to compare the PUFF results with field data of any eruption and/or results of other VATDM (e.g. FALL3D). PUFF is a Lagrangian modeland has been used to date for particle tracking to provide ash dispersalforecasts for explosive eruptions. However, we have demonstratedthat by applying an appropriate statistical approach, the model maybe used in much the same way as any other numerical model (e.g.Eulerian models).

In order to apply the proposed statistical approach, it is necessaryto greatly increase the number of particles N from the default value toNm. However, N may change with the differing characteristics ofdifferent eruptions, computational domains, and meteorologicalconditions. Consequently, Nm should be evaluated any time the initialconditions are significantly modified. In our case, we identified twodifferent scenarios, Scenario 1 and Scenario 2, run daily at INGV-CT forforecasting Etna volcanic plumes (Scollo et al., 2009). Consequentlywe fixed both sets of input parameters and the computationaldomain.

It should be noted that Scenario 2 represents one of the mostexplosive events that has occurred in the last century at Etna volcano.We found that, for a similar event, about 33 M particles should be usedto reach the 99% of the correlation coefficient on the ground (Table 5).This is probably due to the fact that most of particles could be out thedomain or still in air after three hours of simulation. This could explainwhy a smaller number of particles in air are needed in S2with respectto S1. Since this event was sub-plinian in style (Andronico et al.,1999), for volcanic eruptions having a higher intensity (e.g. August1991, Hudson volcano, Chile, (Kratzmann et al., 2010)), Nm should beincreased even only accounting for the necessary increase of thecomputational area. In our case the computed area is 170×170 km2.VATDM usually use a larger domain (order of 1500×1500 km2).Consequently, if the explosive activity is increasing and we are

140 S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

interested in investigating a wider domain, we expect the number ofparticles to increase greatly keeping the same grid resolution.However, it is difficult to make a correlation between Nm andincreasing of explosive activity because in our study S1 and S2 differfor intensity of explosive activity but also for the duration (3 h for S1and 5 min for S2).

In PUFF, N is set at 5000 particles by default. However, many usersin previous analyses increase the number of particles up to 100,000particles (Fero et al., 2008, 2009). Webley et al. (2007) showed thatPUFF is an efficient tool for simulating the distribution of atmosphericash cloud for small eruptions over short time periods using 10,000particles, averaged over 10 simulations. In agreement with Petersonand Dean (2003), the choice of N is a tradeoff between physicalrepresentation and computational requirements. In order to calculatethe deposit load and ash concentration, N has to be at least two ordersof magnitude higher than the previous applications. This requires theuse of parallel computing techniques that are capable of making thiswork manageable. This analysis was made possible using a Beowulfcluster composed of 48 nodes at INGV-CT. In this way, a PUFF outputcontaining 7.5 M volcanic particles is obtained in only a few minutes.

Peterson and Dean (2003) found that the number of simulationsnecessary to create a suitable average among PUFF simulationsproduced from the random-walk process was 50. In our analysis, weaverage 190 values of ρji taking the combination of all possible pairs of20 simulations (Section 2.2). This leads to the question of whathappens if 190 different simulations are taken instead of combina-tions. Therefore, we performed the following test.

We ran 190 simulations for S1-RUN0 (FL120) each having 20 Mparticles (obtained by summing 400 “different” runs with 50,000particles). In this case, the correlation was 94.97%. Instead, using 20 Mparticles obtained by combinations, the correlation was 97%.Consequently, with respect to our forecast, we have an error of onlyabout 2%. If the volcanic particles are further increased to 40 M, thecorrelation is 97.84% whereas the estimated value is 98.5%. Asexpected, our results improve by increasing the number of particles.

Finally, we remark that, from the operational point of view, afterthe Eyjafjallajökull eruption, there is the necessity to evaluate theareas of low (≤2×10−3 g/m3), medium (≥2×10−3 g/m3 and ≤4×10−3 g/m3) and high ash contaminations (≥4×10−3 g/m3) asrequired in the Volcanic Ash Contingency Plan of Europe and NorthAtlantic Regions (ICAO, 2010). Presently, the PUFF outputs are uselessto define the unsafe areas if it is applied as a particle tracking model.The proposed approach allows to obtain quantitative ash concentra-tion maps from PUFF outputs (and any Lagrangian model), useful todefine the No Fly Zone and mitigating the risk caused by volcanic ashencountering.

4.2. The parametric study

The diffuseH parameter (the horizontal diffusion) has a first ordereffect on the PUFF results for both scenarios. The default horizontaldiffusion coefficient is a conservative 10,000 m2/s because PUFF wasdesigned as an operational ash dispersal forecasting tool. Searcy et al.(1998) found a value of 8000 m2/s in order to match the eruption ofRabaul Caldera on 14 September 1994, and a value of 5000 m2/s wasrequired to model the Etna eruption on 22 July 1998 (Daniele et al.,2009). Analyzing the dispersal of volcanic ash from Usu volcano inJapan on 31 March 2000, Tanaka and Yamamoto (2002) found a valueof 100 m2/s. Due to these different results, it is very difficult todetermine predefined values of diffuseH. Consequently, it should beevaluated during the eruption in order to furnish the best fit with theobservations because our parametric study demonstrates how thisinput has a strong influence on the forecasted deposition. We suggestthat a preliminary matching between PUFF simulations and satelliteimages could furnish a preliminary value for diffuseH.

The dtMins parameter used in the Lagrangian time-steppingmethod should be set near 1 min. This parameter is strictly linkedto the eruptive scenarios considered in the study. The only advantagein increasing the value of dtMins is the consequent decrease incomputational time required (Peterson and Dean, 2003). However,parallel computing techniques, as used in this analysis, drasticallyreduce this time.

Topography influences the time at which the particle reaches theground. For weak plumes, the topography parameter (DEM) plays animportant role due to the slower travelling of volcanic particles fromplume to the ground. The effect should decrease with the increase ofthe initial column height. Our results confirm a stronger influence ofthe DEM for weak plumes produced by S1 than strong plumesproduced by S2 (Tables 6 and 7).

The ashLogMean parameter describes the grain-size distribution ofvolcanic particles. Peterson and Dean (2003) showed that particle sizehas the most dramatic effect on model results. However, our testsshow that the ashlogSdev parameter (standard deviation of theparticle size distribution) has a greater effect than the ashLogMeanparameter for both two scenarios. This effect increases with thedecreasing of the particle size in agreement with Peterson and Dean(2003) who found small changes in the standard deviation haverelatively large effects when the particle size is small.

The plumeMax parameter has a small influence on the PUFF results.However, we considered an error in the estimation of the columnheight of only ±1 km because the good monitoring of Etna plumes(e.g. Andronico et al., 2009) allow constraining this parameter with afairly high degree of precision through images mainly obtained fromvideo surveillance carried out by INGV-CT. Results are in agreementwith the findings of Scollo et al. (2009) that small variations of thecolumn height have little influence on the model outputs of HAZMAP,TEPHRA and FALL3D models. It should be highlighted that theuncertainty in plume heights for other volcanoes which are lesswell monitored than Etna could have more important implications onplume dispersal (Papp et al., 2005).

PUFF has three different options for describing the settlingterminal velocities of volcanic ash (“Constant”, “Stokes”, and “Rey-nolds”). In particular, results show that the choice of the threedifferent model options may modify the PUFF results for eruptionshaving high initial eruption columns. Several studies have shown thatterminal settling velocity law has an important role in the pattern ofdeposition (e.g. Pfeiffer et al., 2005) and should be modeledaccurately. Hence, in our opinion, due to the importance of theReynolds number on the thickness variations of tephra fall deposits(Bonadonna et al., 1998), the “Reynolds” law is the preferreddescription. It is also notable that PUFF does not account for twoimportant phenomena that are very common in sedimentationprocesses of volcanic ash: (1) the decreasing in terminal settlingvelocities due to the irregular shape of volcanic ash (e.g. Riley et al.,2003; Coltelli et al., 2008); and (2) the presence of an aggregationphenomenon (e.g. Durant et al., 2009). The first should decreaseterminal velocity values whereas the latter could lead to thepremature fallout of fine ash.

The plumeShape parameter (describing the particle distributionwithin the eruption column) influences the results only for S2. Inagreement with Peterson and Dean (2003), it should be chosenaccurately if eruptions produce a strong plume. However, in the caseof Etna, the majority of events in the last ten years produced weakplumes (Andronico and Scollo, 2008) and this parameter may beconsidered less consequential. Differences in the model results couldbe due to the variation of the particle distribution inside the column.In the literature, there are several empirical methods used in ashdispersal modeling to distribute the mass along the eruption column(e.g. Suzuki, 1983). However, these empirical laws should be revisedand replaced with more reliable models on eruption columndistributions already available in the literature (e.g. Ishimine, 2007).

141S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

4.3. The best-fit

The field data of 2001 Etna eruption (Scollo et al., 2007) haveextensively been used to evaluate the performance of VATDM asFALL3D (Costa et al., 2006), VOL-CALPUFF (Barsotti and Neri, 2008),and HAZMAP (Scollo et al., 2007). Further, input parameters of thisevent have recently been considered as a representative scenario forEtna volcano (Mastin et al., 2009) by the Eruption Source Parametersworkgroup (http://www.esp.images.alaska.edu/index.php). Thesedata are therefore ideal to test the reliability of PUFF model forecasts.Results show that the best fit is obtained using a fine grain-size classreflecting the phreatomagmatic nature of the first phase of Etnaeruption (Scollo et al., 2007). The best fit for the maximum columnheight is 5.5 km. As previously mentioned, this result is very similar tothose obtained by analyzing the MISR images (Scollo et al., 2010),whereas it is higher with respect to the maximum column heightobtained by the geometric analysis of pictures taken during theexplosive event (Scollo et al., 2007). However, it is noted that whilethe error of the MISR height ranges from 0.1 to a maximum of 0.4 km(Naud et al., 2004), the error in the column height observed in thefield may reach 1 km. PUFF also describes well the distribution ofparticles inside the eruption column. We found in fact that the lineardistribution leads to a good fit to the real tephra deposit. In agreementwith models of well mixed weak plumes, such as the 2001 event, therising plume is subjected to a turbulently diffused vertical current inwhich the particles are distributed almost uniformly in the verticaldirection due to a more efficient turbulent mixing and vorticity(Turner, 1973; Bonadonna et al., 2005b).

Lagrangian models such as PUFF are widely used by volcanic ashadvisory centers (VAAC) to reduce risks from volcanic ash dispersal.However, they are usually run with a relatively small number ofparticles forcing them to obtain only qualitative information frommodel results. Instead, our results show that when the number ofparticles is increased, we can calculate the tephra deposit and ashconcentration in air reliability. Results of the best-fit proceduredemonstrate that a Lagrangian model can furnish the same informa-tion as an Eulerian model, making possible any comparisons amongthe model results.

5. Concluding remarks

This work shows that, using a statistical approach, we can calculatetephra deposit load and ash concentration in air by a Lagrangianmodel such as PUFF. We find that for two well defined eruptionscenarios and a small computation domain, up to 33 and 220 millionparticles are necessary to accurately calculate the deposit load and ashconcentration in air, respectively. These values are at least two ordersof magnitude larger than the values typically considered byLagrangian models. Despite the high number of particles, thecomputational time may be drastically reduced using parallelcomputing techniques. Consequently, Lagrangian models could beused to define the volumes of airspace which should be interdicted toaviation operations and improve current strategies of ash forecasting.

The parametric analysis has shown that PUFF results are greatlyaffected by the topography, the horizontal diffusion coefficient, thetime step of the simulations, and the standard deviation of the particledistribution. While the topography needs to be included and the timestep can be set to the minimum value, the horizontal coefficient andthe standard deviation should be set accurately when PUFF is usedoperationally during emergencies.

Finally, a comparison between PUFF simulations and the 2001 fielddata has shown that PUFF may furnish reliable values of the depositload comparable with the results obtained by other volcanic ashdispersal models.

In the future, additional tests should be carried out in order tobetter evaluate how the minimum number of particles Nm is affected

by the eruption size. Finally, a detailed comparison between aLagrangian (e.g. PUFF) and Eulerian model (e.g. FALL3D) should beperformed in a way to evaluate the strength and weakness of the twodifferent approaches.

The proposed approach will allow obtaining quantitative ashconcentration maps from Lagrangian model such us PUFF which arewidely used by VAACs to forecast volcanic ash dispersal and define thecontaminated area for ensuring the safety of the air transportation.

Acknowledgements

The authors thank M. Aloisi for his advices in running PUFF modeland A. Bonaccorso who encouraged the use of PUFF as operative toolfor Etna volcanic ash forecasting. The authors thank the reviewersArnau Folch and Costanza Bonadonna who improved the quality ofthe paper with their constructive suggestions. The native speakerStephen Conway is also thanked. This work was funded by the FIRBItalian project “Sviluppo Nuove Tecnologie per la Protezione e Difesadel Territorio dai Rischi Naturali” of Italian Minister of University andResearch for the three authors (M. Prestifilippo, S. Scollo, G. Spata).

References

Aloisi, M., D'Agostino, M., Dean, K.G., Mostaccio, A., Neri, G., 2002. Satellite analysis andPUFF simulation of the eruptive cloud generated by the Mount Etna paroxysm of 22July 1998. J. Geophys. Res. 107 (B12). doi:10.1029/2001JB000630.

Andronico, D., Scollo, S., 2008. 1998–2007: Ten Years of Explosive Activity at Mt. EtnaVolcano, IAVCEI 2008 General Assembly, Reykjavìk, Island, 18–24 August 2008. .

Andronico, D., Del Carlo, P., Coltelli, M., 1999. The 22 July 1998 fire fountain episode atVoragine Crater (Mt. Etna, Italy). Proceedings of the Volcanic andMagmatic StudiesGroup — Annual Meeting. January 5–6, 1999.

Andronico, D., Scollo, S., Cristaldi, A., Ferruccio, F., 2009. Monitoring ash emissionepisodes atMt. Etna: the 16 November 2006 case study. J. Volcanol. Geoth. Res. 180,123–134.

Barnard, S.T., 2004. Results of a reconnaissance trip to Mt. Etna, Italy: the effects of the2002 eruption of Etna on the province of Catania. Bull. New Zealand Soc.Earthquake Eng. 37 (2), 47–62.

Barsotti, S., Neri, A., 2008. The VOL-CALPUFF model for atmospheric ash dispersal: 2.Application to the weak Mount Etna plume of July 2001. J. Geophys. Res. 113,B03209. doi:10.1029/2006JB004624.

Bonadonna, C., Ernst, G.G.J., Sparks, R.S.J., 1998. Thickness variations and volumeestimates of tephra fall deposits: the importance of particle Reynolds number. J.Volcanol. Geotherm. Res. 81, 173–187.

Bonadonna, C., Macedonio, G., Sparks, R.S.J., 2002. Numerical modelling of tephra falloutassociated with dome collapses and vulcanian explosions: application to hazardassessment on Montserrat. In: lDruitt, T.H., Kokelaar, B.P. (Eds.), The Eruption ofSoufrière Hills Volcano, Montserrat, from 1995 to 1999. Geological Society, London,pp. 517–537. Memoir.

Bonadonna, C., Connor, C.B., Houghton, B.F., Sahetapy-Engel, S., Hincks, T., Connor, L.,2005a. Probabilistic modeling of tephra dispersion: hazard assessment of a multi-phase rhyolitic eruption at Tarawera, NewZealand. J. Geophys. Res. 110, B03203.doi:10.1029/2003JB002896.

Bonadonna, C., Phillips, J.C., Houghton, B.F., 2005b. Modeling tephra sedimentationfrom a Ruapehu weak plume eruption. J. Geophys. Res. 110, B08209. doi:10.1029/2004JB003515.

Casadevall, T.J., 1994. Volcanic ash and aviation safety. Proceedings of the FirstInternational Symposium on Volcanic Ash and Aviation Safety. U.S. GeologicalSurvey Bulletin. 2047, 450.

Cavazzoni, C., Ongaro, T.E., Erbacci, G., Neri, A., Macedonio, G., 2005. High performancecomputing simulations of pyroclastic flows. Comput. Phys. Commun. 169, 454–456.

Charpentier, I., 2008. Variational coupling of Plinian column models and data:application to El Chichon volcano. J. Volcanol. Geotherm. Res. 175, 501–508.

Coltelli, M., Miraglia, L., Scollo, S., 2008. Shape characterization of the volcanic particlescarried out by SEM technique for the calculus of the terminal settling velocities.Bull. Volcanol.. doi:10.1007/s00445-007-0192-8

Costa, A., Macedonio, G., Folch, A., 2006. A three dimensional Eulerian model fortransport and deposition of volcanic ashes. Earth Planet. Sci. Lett. 241, 634–647.

Daniele, P., Lirer, L., Petrosino, R., Spinelli, N., Peterson, R., 2009. Applications of the PUFFmodel to forecasts of volcanic clouds dispersal from Etna and Vesuvio. Comput.Geosci. 35, 1035–1049.

Dean, K.G., Dehn, J., Papp, K.P., Smith, S., Izbekov, P., Peterson, R., Kearney, C., Steffke, A.,2004. Integrated satellite observations of the 2001 eruption of Mt. Cleveland,Alaska. J. Volcanol. Geotherm. Res. 135, 51–73.

Duda, R.O., Hart, P.E., Stork, D.G., 2001. Pattern Classification. Wiley. 2 edition,November 2001.

Durant, A.J., Rose, W.I., Sarna-Wojcicki, A.M., Carey, S., Volentik, A.C.M., 2009.Hydrometeor-enhanced tephra sedimentation: constraints from the 18 May 1980eruption of Mount St. Helens (USA). J. Geophys. Res. 114. doi:10.1029/2008JB005756.

142 S. Scollo et al. / Journal of Volcanology and Geothermal Research 200 (2011) 129–142

Favalli, M., Mazzarini, F., Pareschi, M.T., Boschi, E., 2004. Role of local wind circulation inplumemonitoring atMt. Etna volcano (Sicily): insights from amesoscale numericalmodel. Geophys. Res. Lett. 31. doi:10.1029/2003GL019281.

Fero, J., Carey, S.N., Merrill, J.T., 2008. Simulation of the 1980 eruption of Mount St.Helens using the ash-tracking model PUFF. J. Volcanol. Geotherm. Res. 175 (3),355–366.

Fero, J., Carey, S.N., Merrill, J.T., 2009. Simulating the dispersal of tephra from the 1991Pinatubo eruption: implications for the formation of widespread ash layers. J.Volcanol. Geotherm. Res. 186 (1–2), 120–131.

Folch, A., Cavazzoni, C., Costa, A., Macedonio, G., 2008. An automatic procedure toforecast tephra fallout. J. Volcanol. Geotherm. Res. 177, 767–777.

ICAO, 2010. EUR Doc 019 NAT Doc 006, Part II. Volcanic Ash Contingency Plan, Eur andNat Regions. . July 2010.

Ishimine, Y., 2007. A simple integral model of buoyancy-generating plumes and itsapplication to volcanic eruption columns. J. Geophys. Res. 112, B03210.doi:10.1029/2006JB004274.

Keating, G.N., Pelletier, J.D., Valentine, G.A., Statham, W., 2008. Evaluating suitability ofa tephra dispersal model as part of a risk assessment framework. J. Volcanol.Geotherm. Res. 177, 397–404.

Kratzmann, D.J., Carey, S., Scasso, R., Naranjo, J.A., 2010. Simulations of tephra dispersalfrom the 1991 explosive eruptions of Hudson volcano, Chile. J. Volcanol. Geotherm.Res. 190, 337–352.

Macedonio, G., Costa, A., Longo, V., 2005. A computer model for volcanic ash fallout andassessment of subsequent hazard. Comput. Geosci. 31, 837–845.

Mastin, L.G., Guffanti, M., Servranckx, R., Webley, P., Barsotti, S., Dean, K., Durant, A.,Ewert, J.W., Neri, A., Rose, W.I., Schneider, D., Siebert, L., Stunder, B., Swanson, G.,Tupper, A., Volentik, A., Waythomas, C.F., 2009. A multidisciplinary effort to assignrealistic source parameters to models of volcanic ash-cloud transport anddispersion during eruptions. J. Volcanol. Geotherm. Res. 186, 10–21.

Naud, C., Muller, J., Haeffelin, M., Morille, Y., Delaval, A., 2004. Assessment of MISR andMODIS cloud top heights through intercomparison with a back-scattering lidar atSIRTA. Geophys. Res. Lett. 31, L04114. doi:10.1029/2003GL018976.

Papp, K.R., Dean, K.G., Dehn, J., 2005. Predicting regions susceptible to highconcentrations of airborne volcanic ash in the North Pacific region. J. Volcanol.Geotherm. Res. 148, 295–314.

Peterson, R.A., Dean K., 2003. Sensitivity of Puff: a Volcanic Ash Particle Tracking Model,Technical Report (http://www.puff.images.alaska.edu/sensitivity/sens_paper.pdf).

Pfeiffer, T., Costa, A., Macedonio, G., 2005. A model for the numerical simulation oftephra fall deposits. J. Volcanol. Geotherm. Res. 140 (4), 273–294.

Riley, C.M., Rose, W.I., Bluth, G.J.S., 2003. Quantitative shape measurements of distalvolcanic ash. J. Geophys. Res. 108 (B10), 2504. doi:10.1029/2001JB000818.

Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M.,Tarantola, S., 2008. Global Sensitivity Analysis the Primer. John Wiley & Sons.

Scollo, S., Bonadonna, C., Coltelli, M., Del Carlo, P., 2006. Probabilistic Tephra Fall-hazardAssessment at Etna Volcano, Italy, Cities on Volcanoes 4, Quito, Ecuador, 22–27January 2006. .

Scollo, S., Del Carlo, P., Coltelli, M., 2007. Tephra fallout of 2001 Etna flank eruption:analysis of the deposit and plume dispersion. J. Volcanol. Geoth. Res. 160, 147–164.

Scollo, S., Tarantola, S., Bonadonna, C., Coltelli, M., Saltelli, A., 2008a. Sensitivity analysisand uncertainty estimation for tephra dispersal models. J. Geophys. Res. 113(B06202). doi:10.1029/2006JB004864.

Scollo, S., Folch, A., Costa, A., 2008b. A parametric and comparative study of differenttephra fallout models. J. Volcanol. Geotherm. Res. 176, 199–211.

Scollo, S., Prestifilippo, M., Spata, G., D'Agostino, M., Coltelli, M., 2009. Monitoring andforecasting Etna volcanic plumes. Nat. Hazards Earth Syst. 9, 1573–1585.

Scollo, S., Folch, A., Coltelli, M., Realmuto V.J., 2010. Three-dimensional volcanic aerosoldispersal: A comparison between Multiangle Imaging Spectroradiometer (MISR)data and numerical simulations, J. Geophys. Res. 115, D24210. doi:10.1029/2009JD013162.

Searcy, C., Dean, K., Stringer, W., 1998. PUFF: a high-resolution volcanic ash trackingmodel. J. Volcanol. Geotherm. Res. 80, 1–16.

Suzuki, T., 1983. A theoretical model for dispersion of tephra. In: D.S.a.I.Y. (Ed.), ArcVolcanism, Physics and Tectonics. Terra Scientific Publishing Company TerraScientific Publishing Company Terrapub, Tokyo, pp. 95–113.

Tanaka, H.L., 1994. Development of a Prediction Scheme for Volcanic Ash Fall fromRedoubt Volcano, Alaska. : Proc. First International Symposium on Volcanic Ash andAviation Safety, 2047. U.S. Geological Survey, Bulletin, pp. 283–291.

Tanaka, H.L., Yamamoto, K., 2002. Numerical simulation of volcanic plume dispersalfrom Usu Volcano in Japan on 31 March 2000 using PUFF model. Earth PlanetsSpace 54 (7), 743–752.

Turner, J.S., 1973. Buoyancy effects in fluids. Cambridge University, Press, Cambridge.368 pp.

Webley, P.W., Dean, K., Bailey, J.E., Dehn, J., Peterson, R., 2007. Volcanic ashmodeling forNorth Pacific volcanoes automated operational monitoring and virtual globes. 4th

International Workshop on Volcanic Ash. Civil Aviation Authority, Rotorua, NewZealand, pp. 1–7.

Webley, P.W., Stunder, B.J.B., Dean, K.G., 2009. Preliminary sensitivity study of eruptionsource parameters for operational volcanic ash cloud transport and dispersionmodels — a case study of the August 1992 eruption of the Crater Peak vent, MountSpurr, Alaska. J. Volcanol. Geotherm. Res. 186 (1–2), 108–119.