the eyjafjöll explosive volcanic eruption from a microwave weather radar … · 2015-01-31 ·...

Atmos Chem Phys 11 9503ndash9518 2011wwwatmos-chem-physnet1195032011doi105194acp-11-9503-2011copy Author(s) 2011 CC Attribution 30 License

AtmosphericChemistry

and Physics

The Eyjafjoumlll explosive volcanic eruption from a microwave weatherradar perspective

F S Marzano12 M Lamantea1 M Montopoli 23 S Di Fabio24 and E Picciotti4

1Department of Information Engineering Sapienza University of Rome Rome Italy2Centre of Excellence CETEMPS University of LrsquoAquila LrsquoAquila Italy3Department of Electrical and Information Engineering University of LrsquoAquila Italy4HIMET LrsquoAquila Italy

Received 12 March 2011 ndash Published in Atmos Chem Phys Discuss 20 April 2011Revised 11 August 2011 ndash Accepted 22 August 2011 ndash Published 16 September 2011

Abstract The sub-glacial Eyjafjoumlll explosive volcanic erup-tions of April and May 2010 are analyzed and quantitativelyinterpreted by using ground-based weather radar data andthe Volcanic Ash Radar Retrieval (VARR) technique TheEyjafjoumlll eruptions have been continuously monitored by theKeflaviacutek C-band weather radar located at a distance of about155 km from the volcano vent Considering that the Eyjafjoumlllvolcano is approximately 20 km from the Atlantic Ocean andthat the northerly winds stretched the plume toward the main-land Europe weather radars are the only means to providean estimate of the total ejected tephra The VARR method-ology is summarized and applied to available radar time se-ries to estimate the plume maximum height ash particle cat-egory ash volume ash fallout and ash concentration every5 min near the vent Estimates of the discharge rate of erup-tion based on the retrieved ash plume top height are pro-vided together with an evaluation of the total erupted massand volume Deposited ash at ground is also retrieved fromradar data by empirically reconstructing the vertical profileof radar reflectivity and estimating the near-surface ash fall-out Radar-based retrieval results cannot be compared withground measurements due to the lack of the latter but furtherdemonstrate the unique contribution of these remote sensingproducts to the understating and modelling of explosive vol-canic ash eruptions

Correspondence toF S Marzano(marzanodietuniroma1it)

1 Introduction

The early detection and quantitative retrieval of volcanic ashclouds is both a scientific and practical issue which can havesignificant impacts on human activities Volcanic eruptionscan represent a serious socio-economic and a severe environ-mental hazard (Graf et al 1999 Durant et al 2010) Plumeheight reaching typical altitudes of modern aerial routes canaffect flight safety and have huge knock-on effects on airtraffic control making necessary the re-routing of airways(Prata and Tupper 2009) The volcanic eruptions may haveboth short-term effects regarding health threats to people liv-ing in the area near the volcano and long-term effects sinceairborne ash clouds may affect both surface ocean biogeo-chemical cycles and control atmospheric feedbacks of cli-mate trend (Robock 2000 Duggen et al 2010)

The previously described risk scenario has become unfor-tunately a reality in the spring 2010 during the last Eyjafjoumlllvolcanic eruption which was the largest explosive eruptionin Iceland since that of the Hekla volcano in 1947 (Pe-tersen 2010) The 2010 Eyjafjoumlll eruption featured both aninitial phreato-magmatic phase (characterized by the pres-ence of juvenile clasts resulting from the interaction be-tween magma and water) and predominantly magmatic re-maining phases (Guethmundsson et al 2010) Unlike previ-ous Icelandic events the 2010 Eyjafjoumlll eruption lasted sev-eral weeks sustaining an average magma discharge of sev-eral hundred tonnes per second and producing large quanti-ties of lapilli coarse fine and very fine ash particles whichwere advected towards south and south-east along the majorEuropean air traffic routes causing an unprecedented flightcrisis (Gertisser 2010)

A quantitative measurement and analysis of volcanic ashcloud physical and chemical properties is crucial (Durantet al 2010) Any decision support system for both civil

Published by Copernicus Publications on behalf of the European Geosciences Union

9504 F S Marzano et al The Eyjafjoumlll explosive volcanic eruption

protection and air traffic management needs not only a de-tection of the erupted and dispersed ash cloud but also theestimation and forecast of its ash content (Prata and Tup-per 2009) The Eyjafjoumlll eruption on 2010 has been oneof the best documented European volcanic events in termsof ground and satellite observations (eg Ansmann et al2010 Bennet et al 2010 Flentje et al 2010 Gasteiger etal 2011 Guethmundsson et al 2010 Madonna et al 2010Mona et al 2010 Schumann et al 2011 Pietruczuk et al2010 Stohl et al 2011) Particular importance is devoted tothe ldquonear-sourcerdquo (where the ldquosourcerdquo is the volcano vent)instrumentation as measured data can be used to properlyinitialized ash-plume dispersion models (eg Bonadonna etal 2009 Costa et al 2006 Stohl et al 1998) Coarse ashand lapilli are expected to fall within few hours from ejec-tion time into air and within distances less than few hun-dreds of kilometres from the volcanic vent (Rose and Du-rant 2009) This deposited tephra (ie the fragmental ma-terial produced by a volcanic eruption) is typically estimatedto be more than 99 of the total ash mass (Wen and Rose1994) Advanced volcanic sites can deal with an ensem-ble of ldquonear-sourcerdquo synergetic instruments (Sparks et al1997 Zehner 2010) in situ drillings and sondes surveil-lance flights for plume monitoring GNSS (Global Naviga-tion Satellite System) differential receivers for deformationmeasurements seismic signal receivers for tremor analysisinterferometric synthetic aperture radars (InSARs) for de-formation imaging ground-based lidars ceilometers pho-tometers and microwave radars for plume probing very-low-frequency (VLF) receivers for lightning detection and satel-lite infrared radiometers for broadscale plume tracking EvenUnmanned airborne vehicles (UAVs) cannot be used to probethe near-source tephra due to inherent risks (Schumann et al2011) Satellite visible and thermal infrared split-windowtechniques may miss ldquonear-sourcerdquo tephra as they are basi-cally insensitive to ash particles larger than few tens of mi-crons (Yu et al 2002 Pavolonis et al 2006 Kahn et al2007 McCarthy et al 2008 Stohl et al 2010) On the otherhand ground-based optical ldquonear-sourcerdquo observations maybe completely opaque due to the strong extinction of coarseand large ash particles (Zehner 2010)

ldquoNear-sourcerdquo observations if available do not gener-ally include estimates on the ash plume volume and concen-tration The magma discharge estimate is primarily basedon an empirical relationship established between observederuption column heights derived from ground-based weatherradars and magma discharge (Lacasse et al 2004 Odds-son et al 2009) Estimates on concentration of ash solidmaterial in the eruption plume are usually based on theoret-ical assumptions which may be supported by satellite-basedobservations of the ash cloud at mid to far distances (hun-dreds of kilometres) from the vent (Wilson 1972 Sparkset al 1997) In this context active microwave remote sens-ing through ground-based scanning weather radars can bebetter exploited and can represent a very powerful and to

some extent unique instrument to study explosive eruptionsin proximity of volcanic vents (Harris and Rose 1983 La-casse et al 2004 Marzano et al 2006a Gouhier and Don-nadieu 2008) In the ldquonear-sourcerdquo region weather radarsmay be capable to provide in principle not only the plumeheight but also ash particle category ash volume ash fall-out and ash concentration (Marzano et al 2006b 2010b2011a) Conventional weather radar targets are precipitatinghydrometeors whose shape dimension and dielectric proper-ties are undoubtedly different from tephra ones (Sauvageot1992) This implies that weather radars cannot be used forash cloud monitoring without developing ad hoc inversionmethodologies and techniques to process radar data streamAmong these algorithms the VARR (Volcanic Ash RadarRetrieval) approach has been shown to be a relatively generaltheoretical and operational framework to infer in a quantita-tive way ash mass category concentration and fallout ratefrom three-dimensional (3-D) scanning weather-radar mea-surements (Marzano et al 2006b 2010a) The VARR prod-ucts must be carefully treated as any remote sensing inver-sion methodology they are obtained under proper physical-statistical assumptions and given sensor limitations (eg re-ceiver sensitivity and polarization agility)

The potential of VARR data processing in observing vol-canic ash clouds has been analyzed using some case studieswhere volcano eruptions happened near an available weatherradar (i) the Griacutemsvoumltn volcano eruption in 2004 analyzedtogether with the Icelandic Meteorological Office (IMO) us-ing a C-band weather radar (Marzano et al 2006b 2010a2010b) (ii) the Augustine volcano eruption in 2006 ana-lyzed together with the US Geological Survey Alaska Vol-cano Observatory using an S-band weather radar (Marzanoet al 2010b) This work presents new results of the VARRmethodology applied to the sub-glacial explosive eruptionsof Icelandic Eyjafjoumlll stratovolcano whose maximum activ-ities occurred on April and May 2010 The 2010 eruptionshave been monitored and measured by the Keflaviacutek C-bandweather radar at a distance of about 155 km from the vol-cano vent (Guethmundsson et al 2010) The distance be-tween the Eyjafjoumlll volcano and the Icelandic coast is ap-proximately 20 km Due to the proximity between the vol-cano and the Atlantic Ocean and the prevailing northerlywinds which stretched the plume toward the mainland Eu-rope collecting ground data samples in order to estimate thetotal ejected tephra or the ash distribution is not an easy taskespecially in the nearby of the Eyjafjoumlll volcano In this re-spect weather radar is one of the most powerful instrumentsto investigate this phenomenon and estimate the near-sourceash fallout

This paper is structured as follows In Sect 2 the Ey-jafjoumlll eruptions of April and May 2010 are described andthe effects of the volcanic plume are summarized Moreoverradar data are discussed and VARR algorithm data process-ing features are briefly introduced In Sect 3 weather radarretrievals with reference to time and spatial volcanic cloud

Atmos Chem Phys 11 9503ndash9518 2011 wwwatmos-chem-physnet1195032011

F S Marzano et al The Eyjafjoumlll explosive volcanic eruption 9505

products are presented discussed and compared LastlySect 4 is dedicated to conclusions and tracing future researchand development perspectives

2 Data and methodology

The Eyjafjoumlll stratovolcano is located under the Eyjafjalla-joumlkull ice cap a small glacier within the Icelandic East Vol-canic Zone (Larsen et al 1998 Pedersen and Sigmundsson2006) The latter is the most active of the four Icelandic vol-canic zones due to its position over the Mid-Atlantic Ridgethe divergent tectonic plate boundary between the EurasianPlate and the North American Plate (Thordarson and Larsen2007) The eruptions in 2010 lasted several weeks startingat the end of March with precursors event (such as seismicactivities) since the end of 2009 on April 2010 and May2010 the activity of the volcano reached its peak levels withsome explosive eruptions (Guethmundsson et al 2010 Pe-tersen 2010)

21 Volcanic eruptions on April and May 2010

The Eyjafjoumlll eruptions in 2010 were preceded by seismicactivities around December 2009 that increased at the endof February 2010 (Guethmundsson et al 2010) These earth-quakes were followed by the first magma pourings into themagma chamber of the volcano In the first phase of theeruption from 20 March to 1 April some fissures openedin Fimmvoumlrethuhaacutels (on the eastern flank of Eyjafjoumlll volcano)over the glacial ice The eruption was rated through the vol-canic explosivity index (VEI a relative logarithmic measureof the explosiveness of volcanic eruptions with value 0 fornon-explosive eruptions and 8 for colossal ones) as VEI 1due to the effusive sub-glacial and weak volcanic activitiesand was precursory with respect to the second more signif-icant eruption phase The latter lasted from 14 April until20 May and was rated VEI 4 thus being 40 times more pow-erful than the first phase (Guethmundsson et al 2010)

On 14 April at 0600 UTC the Eyjafjoumlll volcano resumederupting after a small hiatus due to the main eruption siteposition under the centre of the glacier the eruption becameexplosive and phreatomagmatic (Guethmundsson et al 2010Petersen 2010) People living and working in the nearbyareas were evacuated in order to avoid potentially lethal en-counters with the released glacier burst (or joumlkulhlaup in Ice-landic) and the large-scale discharge of melt water reachingthe sand on the lowland plains (or sandur) to the north of thevolcano On 15 April the ash cloud reached mainland Eu-rope thus forcing the closure of airspace over a large partof the United Kingdom Scandinavia and Northern EuropeThe eruption tremors continued at a similar level to thoseobserved immediately before the start of the second erup-tion phase On 16 and 17 April a pulsating eruptive columnreached above 8 km altitude with a maximum of 13 km be-

fore the plume height decreasing to 5 km that was too low tolet it travel across Europe On 18 April the seismic activi-ties continued but the eruption further decreased (droppedby an order of magnitude) becoming magmatic (implyingthat external water no longer had ready access to the vents)with a maximum plume until 0800 UTC lower than 3 km asrecorded by the IMO On 19 April the Eyjafjoumlll started toerupt lava flows that slowly melted their way through the iceof the Giacutegjoumlkull outlet glacier and the plume reached again analtitude of 5 km spreading to south direction due to northerlywinds On 20 April the GPS stations around Eyjafjallajoumlkullshowed a deflation associated with the eruption In the fol-lowing nine days the eruption became discontinuous withincreasing and decreasing tremors activities as reported bythe IMO and the ash plume rose up to few kilometres (oftennot exceeding the height of the cloud cover at about 5 km al-titude) with mild explosive activity and light ash fall Duringthese first two weeks continued widespread and unprece-dented disruption to flights and closure of some airports oc-curred both in Iceland and many European countries (Ger-tisser 2010)

On the beginning of May a lava producing phase largerthan the explosive phase started Plume became darkerdenser and wider than in the preceding week with an in-creased tephra fall out near the volcano and an eruptionplume extended to altitudes between 4 km and 6 km (Gueth-mundsson et al 2010 Petersen 2010) On 5 and 6 MayIMO stated that the volcano had entered a new phase with ashift back from lava to more ash production An increase inexplosive activity and considerable ash fall out was reportedat a distance of about 70 km from the eruption site Plumeswere observed at altitudes between 55 km and 65 km reach-ing a maximum height of 9 km On 7 and 8 May the erup-tion was still in a strong explosive phase although its explo-sive activity decreased compared to the previous days theash plume was rising to a lower altitude and was lighter incolor On 9 May the ash cloud reached its stretching max-imum In northern Spain (2000 km from Iceland) and otherwestern European countries (Ireland France and Portugal)the ash cloud forced several airports closures On 10 Maythe ash cloud rose up to between 5 km and 6 km (with somefiner particles rising up to 9 km) and in the following daysit became darker and was headed in a south-easterly direc-tion Since 21 May the eruptive vent emitted a column ofsteam (water vapour) plus sulphurous gases with an eruptioncolumn confined mostly in the proximity of the crater nofurther report of any ash fall from the surrounding area havebeen registered This phase of low activity and quiet state ofthe eruption was officially declared over on October

wwwatmos-chem-physnet1195032011 Atmos Chem Phys 11 9503ndash9518 2011


22 C-band weather radar data

Weather radar systems although designed to study hydrom-eteors and rain clouds can be used to monitor and mea-sure volcanic eruptions parameters (Harris and Rose 1983Marzano et al 2006a) The measured radar backscatteredpower from a volume bin at ranger zenith angleθ and az-imuth angleφ is proportional to the co-polar horizontally-polarized reflectivity factorZH (mm6 mminus3) which is ex-pressed for an ensemble of spherical particles under theRayleigh scattering assumption (Sauvageot 1992)

ZH(rθϕ) =λ4

π5|Kε|2ηH(rθϕ) sim=

D2intD1

D6NaX(D)dD = m6 (1)

whereλ is radar wavelengthKε is the particle dielectric fac-tor (depending on its composition)ηH is the horizontally-polarized reflectivityD is the equivolume spherical parti-cle diameterNaX is the particle size distribution (PSD) andm6 is the PSD sixth moment The latter can be modelled asScaled Gamma (X = SG) or Scaled Weibull PSD (X = SW)characterized by 3 parameters the particle-number mean di-ameterDn (mm) the ash concentrationCa (g mminus3) and thePSD shape coefficient micro (Marzano et al 2006a Sparks et al1997) From Eq (1) keeping constant the ash particle distri-bution the reflectivity factorZH tends to be higher for biggerparticles It is worth noting that the last approximation is notalways valid as particle Mie backscattering effects may needto be taken into consideration depending on the ash cloud for-mation and the radar wavelength (Sauvageot 1992 Marzanoet al 2006a) The measured reflectivity factorZHm can besimulated from the theoretical oneZH in Eq (1) by intro-ducing instrumental and model representativeness errors thelatter being usually modelled as a multiplicative zero-meanGaussian noise (in linear units) Note that dual-polarizationweather radars can offer the potential to measure not onlyZH but also vertically-polarized reflectivity and differentialphase shift which may be useful to better characterize ashparticle properties and non-spherical shape (Marzano et al2011b) Weather radar volume samples as in Eq (1) areacquired by using discrete time and space steps All radar-based retrieved geophysical parameters require the knowl-edge of data spatial and temporal resolution Concerning thespatial resolution the range bin size is proportional to thepulse width whereas its transverse resolution quadraticallyincreases with the radar range (Sauvageot 1992) Tempo-ral resolution is usually constant (here about 5 min) so thatNs radar volume scan temporal samples are available withsampling time step1ts depending on the considered timeinterval

The eruption was detected and monitored during its wholelife span by the C-band (6 GHz) weather radar in Keflaviacuteklocated 155-km north-westwards far away from the calderaof Eyjafjoumlll volcano (eg Lacasse et al 2004 Marzanoet al 2010b) The Keflaviacutek C-band radar volumes were

available from the IMO every1ts = 5 min with reference tothe two more significant time windows of the event since0100 UTC (Universal Time Coordinated) on 14 April 2010till 2355 UTC on 20 April 2010 and since 0010 UTC on5 May 2010 till 2355 UTC on 10 May 10 2010 Ten eleva-tion angles were routinely available (specifically 05 0913 24 35 45 60 80 100 and 150) The radardataset consists of a total ofNs = 3730 volumes in sphericalcoordinates with 10 elevation angles 420 azimuth angles and120 range bins the latter having a range width of about 2 km

Eight of the most significant Horizontal-Vertical Maxi-mum Indicator (HVMI) recorded radar reflectivity imagesare shown in Fig 1 with reference to the time window ofApril and Fig 2 with reference to the time window of MayThe maximum values of the detected reflectivity are pro-jected on the surface as a PPI (Plan Position Indicator) geo-referenced radial map (right-bottom panel) and projected ontwo orthogonal planes along the vertical (top and left sideof the HVMI image) The ash plume is visible over theEyjafjoumlll especially by looking at the upper section (show-ing the north-south profile of the plume) and the left section(showing the east-west profile of the plume) The detectedvolcanic cloud is distinguishable from undesired ground clut-ter and rain cloud returns especially when looking at theHVMI vertical sections Ground clutter can be easily recog-nized from HVMI as it tends to be stationary from an imageto another On the contrary precipitating clouds have a re-flectivity signature quite similar to ash clouds and the mix ofthe two is difficult to treat In the case of 2010 Eyjafjoumlll eventthe observed temporal sequence indicates a distinct ash fea-ture erupted from the volcano vent which can be effectivelydetected

23 Weather radar data processing

The VARR approach foresees 2 steps (i) ash classification(ii) ash estimation Both steps are trained by a physical-electromagnetic forward model basically summarized byEq (1) where the main PSD parameters are supposed tobe constrained random variables (Marzano et al 2006b2010a) The generation of a simulated ash-reflectivity datasetby letting PSD parameters to vary in a random way can beframed within the so called Monte Carlo techniques

Automatic discrimination of ashes classes with respect toaverage diameterlt Dn gt and with respect to average con-centrationlt Ca gt implies the capability of classifying theradar volume reflectivity measurements into one of theNc

classes In order to optimize and adapt the retrieval algo-rithm to the Icelandic scenario VARR has been statisticallycalibrated with ground-based ash size distribution samplestaken within the Vatnajoumlkull ice cap in 2005 and 2006 af-ter the Griacutemsvoumltn last eruption occurred in November 2004(Oddsson et al 2009) since ground PSD data from theEyjafjoumlll eruption are still quite limited (eg Stohl et al2010) Optimal values of PSD parameters have been adopted



19

1

2

3

4 Fig 1 Eight of the most significant HVMI radar images showing the recorded Keflaviacutek C-band radar 5 reflectivity from April 14 2010 at 1455 UTC till April 19 at 2345 UTC See text for details 6 Fig 1 Eight of the most significant HVMI radar images showing the recorded Keflaviacutek C-band radar reflectivity from 14 April 2010 at

1455 UTC till 19 April at 2345 UTC See text for details



20

1

2

3

4 Fig 2 Eight of the most significant HVMI radar images showing the recorded Keflaviacutek C-band radar 5 reflectivity from May 5 2010 at 0640 UTC till May 10 at 0125 UTC See text for details 6 Fig 2 Eight of the most significant HVMI radar images showing the recorded Keflaviacutek C-band radar reflectivity from 5 May 2010 at

0640 UTC till 10 May at 0125 UTC See text for details



through best fitting of SG-PSD and SW-PSD on measuredPSD for each ash diameter class (Marzano et al 2011a)In summary within each of theNc = 9 ash classes we havesupposed a Gaussian random distribution for (i)Dn withaverage valuelt Dn gt equal to 0006 00641 and 05825 mmfor fine coarse and lapilli ash respectively a standard de-viation σDn = 02 lt Dn gt and a corresponding variabilityof 0001le Dn lt006 mm 006le Dn lt 05 mm and 05 le

Dn le 70 mm (ii) Ca with mean valuelt Ca gt equal to 011 and 5 g mminus3 for light moderate and intense concentrationregimes respectively and a standard deviationσCa= 05lt

Ca gt The ash densityρa has been put equal to an averagevalue of 1200 kg mminus3 The optimal PSD shape parameter microhas been set to 09 11 and 14 for fine coarse and lapilliparticles Table 1 summarizes the modelled ash classes

Within the VARR methodology ash classification is per-formed by the use of the MAP (Maximum A Posteriori Prob-ability) estimation (Marzano et al 2006b) The probabilitydensity function (PDF) of each ash class (c) conditionedto the measured reflectivity factorZHm can be expressedthrough the Bayes theorem The MAP estimation of ashclassc corresponds to the maximization with respect toc

of the posterior PDFp(c|ZHm) Under the assumption ofmultivariate Gaussian PDFs the previous maximization re-duces to the following minimization which provides an ashclass for a given volume bin centred in (r θ ϕ)

c(rθϕ) = Minc

[ZHm(rθϕ)minusm(c)Z ]

2(σ

(c)Z

)2+ ln

(σ

(c)Z

)2minus2lnp[c(rθϕ)]

(2)

where Minc is the minimum value with respect toc m(c)Z and

σ(c)Z are the reflectivity mean and standard deviation of class

c whereasp(c) is the a priori PDF of classc and the ash classperturbations have been assumed uncorrelated ComputingEq (2) requires knowledge of the reflectivity mean (m

(c)Z )

and standard deviation (σ(c)Z ) of each ash classc derived

from the 9-class simulated synthetic data set previously de-scribed

For each radar volume bin the ash fallout rateRa(kg mminus2 sminus1) and ash concentrationCa (g mminus3) can be the-oretically expressed by

Ra=

D2intD1

va(D)ma(D)NaX(D)dD

Ca=

D2intD1

ma(D)NaX(D)dD

(3)

whereva(D) is the terminal ashfall velocity in still air (whenthe vertical component of the air speed is neglected) andmais the actual ash mass particle (typically approximated by anequivolume sphere) A power-law dependence ofva on D

is usually assumed in Eq (3) egva = avDbv as shown in

Marzano et al (2006b) from Harris and Rose (1983) the bestfitting providesav = 5558 m sminus1 and bv = 0722 whereasfrom Wilson (1972)av = 7460 m sminus1 andbv = 10

The inversion problem to retrieveCa andRa from ZHm isill-posed so that it can be statistically approached (Marzanoet al 2006b) Through the training forward model as inEq (1) a regressive approximation may be used as a functionof the classc for both Ca and Ra for a given volume bincentred in (r θ ϕ)R

(c)a (rθϕ) = ccZ

dc

Hm(rθϕ)

C(c)a (rθϕ) = acZ

bc

Hm(rθϕ)

(4)

whereZHm is the measured reflectivity factor andacbc cc

anddc are the regression coefficients derived from simulatedtraining dataset

Sensitivity of weather radar observations to ash size andconcentration is dependent on the transmitted wavelengthand receiver Minimum Detectable Signal (MDS) whichin turn is quadratically dependent on the inverse range(Sauvageot 1992 Marzano et al 2006b) Numerical anal-ysis has shown that intense concentration of fine ash (about5 g mminus3 of average diameter of 001 mm) can be detected bya typical C-band radar 50 km far from the ash plume whereassmaller concentrations are not usually retrieved (Marzano etal 2006b) This limitation may be overcome for the sametransmitted power by either reducing the range or increasingthe receiver sensitivity or decreasing the wavelength or radi-ally averaging data Another major problem is the incapabil-ity to discriminate between pure ash particles and aggregatesof ash and hydrometeors (such as cloud ice and water) usingsingle-polarization radar data only as evident from Figs 1and 2 Apart from the use of a priori information such asthe freezing level and satellite-based imagery which are notalways available (Marzano et al 2010b) we can take intoaccount these effects only as a larger uncertainty within themodelled Gaussian noise with a total standard deviation of24 dBZ A more robust VARR inversion algorithm will ex-hibit of course a larger estimate error variance

3 Ash cloud retrieval

The VARR technique can be applied to each radar reso-lution volume in three-dimensional (3-D) spherical coordi-nates where the measured C-band reflectivityZHm(r θ φ)is larger than the minimum detectable reflectivity (MDZ)as discussed in Marzano et al (2006b 2010a) From theKeflaviacutek radar specifications at a range of about 155 kmwhich corresponds to the Eyjafjoumlll volcano vent MDZ isabout minus6 dBZ From the mentioned analyses this MDZimplies that radar echoes are sensitive to coarse ash andlapilli concentration but not necessarily to moderate andlight (lt5 g mminus3) fine ash distribution (Marzano et al 2006b2010a)



Table 1 Ash classes features in terms of average ash diameterlt Dn gt and concentrationlt Ca gt The variability within each class isGaussian with a deviation proportional to the meanσDn = 02lt Dn gt andσCa= 05lt Cagt

ASH CLASSES Light concentration Moderate concentration Intense concentrationlt Ca gt= 01 g mminus3 lt Cagt = 10 g mminus3 lt Cagt = 50 g mminus3

Fine ash size FA-LC FA-MC FA-IClt Dn gt = 0006 mm c = 1 c = 2 c = 3

Coarse ash size CA-LC FA-MC CA-IClt Dn gt = 0064 mm c = 4 c = 5 c = 6

Lapilli particle size LP-LC LP-MC LP-IClt Dn gt = 0583 mm c = 7 c = 8 c = 9

Only PPIs at the first 7 available elevation angles (ie05 09 13 24 35 45 and 60) have been usedas the other ones were useless since radar beam heights didnot intercept the ash plume at higher elevations (see Figs 1and 2) Raw reflectivity data were averaged to about 2-kmradial resolution in order to enhance the signal-to-noise ratioand thus reduce the MDZ The VARR products in terms ofash concentrationCa and falloutRa are originally providedwithin 3-D spherical coordinates (rθ φ) reference systemRadar returns have then been geo-located into a new refer-ence system (λϕ z) whereλ is the longitudeϕ is the lat-itude andz terrain height Spherical coordinates have beenconverted into longitude and latitude through the inversion ofthe ldquohaversinerdquo formula used to compute the great-circle dis-tance (ie the shortest distance over the surface of the Earth)between two points

ϕ =180

π

[asin

(sin(ϕR)cos

(r

Re

))+cos(ϕR)sin

(r

Re

)cos(φ)

](5)

λ =180

π

[λR

180

π+atan2

(sin(φ)sin

(r

Re

)cos(ϕR)cos

(r

Re

)minussin(ϕ)sin(ϕR)

)]whereλR (decimal deg) andϕR (decimal deg) are the Ke-flaviacutek radar longitude and latitude in decimal degrees (re-spectivelyminus2264 and 6403) asin is the arcsine func-tion atan2 is the four quadrant inverse tangent (arctangent)function and 180π converts radians into decimal degreesSupposing a standard atmosphere for electromagnetic wavespropagation the terrain altitudez can be derived by

z =

radicr2+R2

e +2rResin(θ)minusRe+zR (6)

wherezR (m) is the radar height above sea level (47 m in ourcase) andRe= (43)RT is the equivalent Earth radius givenby the so called ldquo43 refraction modelrdquo whereRT (km) isthe Earth radius (Sauvageot 1992) The Eq (6) states thatthe radar beam height is range and elevation angle depen-dent whenr andθ increase the detected altitudes increaseso that only some of the elevation angles can be used due tothe large radar-volcano distance and the expected maximumplume heights A finer grid (λ ϕz) has been generated inorder to allow an easier data geolocation

31 Retrieval time series

The instantaneous volcanic ash cloud volumeVa(t) (m3)which represents the volume of the ash cloud at a given timestept (the latter is referred to as ldquoinstantaneousrdquo even thoughthe radar employs about 2 minutes to complete a volumescan) may be estimated by using a thresholdCath on the es-timated concentrationCa(λ ϕz t) at a given position (λ ϕz) as follows

Va(t) equiv

intCa(λφzt)geCath

dV (7)

wheredV (m3) is the elementary volume The radar-derivedtotal volumeVaT (m3) can then be computed by integratingVa(t) with respect to the initial and final time steps of thevolcanic eruption

The instantaneous volumeVa(t) in (7) should be indeeddistinguished into the ldquodetectedrdquo volumeVad(t) and a ldquohid-denrdquo (non-detected) volumeVah(t) (eg see Figs 1 and 2)In generalVa(t) = Vad(t) + Vah(t) due to the radar obser-vation geometry and the presence of occlusions along theray paths The termVah implies that the total portion ofthe ash cloudVa(t) may not be detectable by the scanningradar thus inducing an underestimation of the total ash vol-ume and mass This problem which is clearly visible inFigs 1ndash2 by looking at HVMI horizontal and vertical pro-jections and is worse at larger distances is a well knownproblem in radar meteorology and it is often overcome re-lying on the reconstruction of the Vertical Profile of Reflec-tivity (VPR) (Sauvageot 1992 Marzano et al 2004) Anapproximate way to approach the VPR problem is to projectthe measured reflectivityZHm available at the lowest rangebin down to the terrain height atz = zs assuming that thelowest detectable value is the major responsible of ash fall-out deposited on the ground from the vertical column above aconsidered position To some extent this approach is similarto that adopted when estimating the total mass from satellitethermal-infrared radiometers when estimates of ash cloud toplayers are extrapolated to ground (Wen and Rose 1994 Yu



21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]

Instantaneous mass trend by VARR on April

05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]

Instantaneous mass trend by VARR on May

1 Fig 3 Instantaneous mass (obtained from ash rate Ra estimated by VARR) versus time expressed in terms of 2 scan days with reference to the eruptions on April (upper panel) and May (lower panel) The ticks on the x-axis 3 have a spacing equal to six hours The scan sampling period is equal to 5 minutes so that the time series shows a 4 time window of about 10020 minutes (equal to 167 hours) since the first available radar data at 0100 UTC on 5 Apr 14 2010 with reference to the dataset of April and about 8630 minutes (equal to 1438 hours) since the first 6 available radar data at 0010 UTC on May 5 2010 with reference to the dataset of May 7

8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]

Instantaneous volume trend by VARR on April

05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]

Instantaneous volume trend by VARR on May

9 Fig 4 Instantaneous volume versus scan days with input data from VARR algorithm with concentration 10 threshold (Cagt10-6 kgm3) In the upper panel the trend with reference to April time window (since 0100 UTC 11 on April 14 2010 till 2355 UTC on April 20 2010) in the lower panel the trend with reference to May time 12 window (since 0010 UTC on May 05 2010 till 2355 UTC on May 10 2010) 13

14

Fig 3 Instantaneous mass (obtained from ash rateRa estimated byVARR) versus time expressed in terms of scan days with referenceto the eruptions on April (upper panel) and May (lower panel) Theticks on the x-axis have a spacing equal to six hours The scan sam-pling period is equal to 5 min so that the time series shows a timewindow of about 10 020 min (equal to 167 h) since the first avail-able radar data at 0100 UTC on 14 April 2010 with reference to thedataset of April and about 8630 min (equal to 1438 h) since the firstavailable radar data at 0010 UTC on 5 May 2010 with reference tothe dataset of May

et al 2002) In both approaches we are neglecting the finitetime interval that a radar resolution volume (bin) of ash takesto reach the ground (given an ash terminal velocity) Notethat the latter coupled with the horizontal transport effectsmay cause a displacement between the radar measure and theactual ash deposition at the ground

UsingVa(t) the instantaneous ash massMa(t) (kg) fromeach radar 3-D volume is given by

Ma(t) equiv

intVa(t)

Ca(λφzt)dV= ρaVa(t) (8)

whereρa (kg mminus3) is the ash density assumed to be constantand equal to about 1200 kg mminus3 The temporal trend of theinstantaneous total massMa(t) retrieved from VARR anddefined in Eq (7) is shown in Fig 3 with reference to bothavailable datasets on April and May 2010 The instantaneousvolume temporal trends obtained from Eq (7) are shown inFig 4 for the same time windows as in Fig 3

These plots are useful to estimate the intensity of the vol-canic eruption in near real-time mode The scan samplingperiod is equal to 5 min so that the time series shows a timewindow of about 10 020 min (equal to 167 h) since the firstavailable radar measurements at 0100 UTC on 14 April 2010with reference to the dataset of April and about 8630 min(equal to 1438 h) since the first available radar measure-ments at 0010 UTC on 5 May 2010 with reference to the

21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14

Fig 4 Instantaneous volume versus scan days with inputdata from VARR algorithm with concentration threshold (Ca gt

10minus6 kg mminus3) In the upper panel the trend with reference to Apriltime window (since 0100 UTC on 14 April 2010 till 2355 UTC on20 April 2010) in the lower panel the trend with reference to Maytime window (since 0010 UTC on 5 May 2010 till 2355 UTC on10 May 2010)

dataset of May Both Figs 3 and 4 shows that the erup-tion peak on April 2010 was at the beginning of the 16thday where ash mass up to 15middot108 kg was estimated Duringthe May episode the most intense day was on 5 May with ashmass up to 8middot107 kg It is interesting to note (i) the intermit-tent and pulsed temporal character of the Eyjafjoumlll eruptionespecially during the April volcanic activity (ii) the abruptdecrease of erupted mass at the end of 16 April (iii) thelonger and gradually decrease tail of the May event whichlasts more than 6 days

The spatial distribution of the instantaneous maximumplume heightHa(λ ϕ t) (km) can be then derived by usingeither a thresholdZHmth on the measured reflectivityZHm(λϕ z t) or a thresholdCath onCa(λ ϕ z t) as follows

Ha(λφt) equiv

Maxz [z|ZHm(λφzt) ge ZHmth]Maxz [z|Ca(λφzt) ge Cath]

(9)

where Maxz is the maximum operator with respect toz Thetwo approaches do not necessarily provide the same resultas will be shown later due to the different and independentadopted thresholds The maximum heightHaM of Ha(λ ϕt) with respect to any (λ ϕ) in Eq (9) is provided by

HaM(t) equiv Maxλφ [Ha(λφt)] (10)

where Maxλϕ is the maximum operator with respect to (λϕ) The maximum heightHaM can be also referred to thespatial sub-domain around the volcano vent The analysis ofthe maximum plume heightHaM is both an important input



parameter in a plenty of volcanological models which fore-cast the volcanic eruption intensity and the most useful quan-tity to aerial routes planning in the areas near the volcaniceruption (Stohl et al 2010) Plinian and sub-Plinian explo-sive eruptions reach their neutral level (above this height thecloud stops its vertical growth and starts to spread radially)at the same altitude of modern commercial airplanes flightlevel (Sparks et al 1997) The merging of local VAACs(Volcanic Ash Advisory Centres) information with the infor-mation about the plume height estimated by meteorologi-cal forecast centres can be very useful to produce more ac-curate and precise VA-SIGMET (Volcanic Ash SIGnificantMETeorological event information) reports (Prata and Tup-per 2009)

The temporal evolution of the maximum plumeheight HaM during a time interval from 0100 UTC on14 April 2010 till 2355 UTC on 20 April 2010 and from0010 UTC on 5 May 2010 till 2355 UTC on 10 May 2010is shown in Fig 5 with 5-min resolution The two plotsshow the estimates of VARR algorithm with detectionthresholds on concentration (Cagt 10minus3 g m3) with referenceto April (upper panel) and May (lower panel) eruptionsAll the altitudes are scaled with reference to the Eyjafjoumlllheight above sea level (1666 m) Figure 6 shows the same ofFig 5 but by using Eq (9) with a detection thresholds onreflectivity (ZHm gt minus6 dBZ) The plume height estimationshows a certain variability also due to the altitude discretesampling of radar beams at given elevations Indeed thedegraded radial resolution (about 2 km in our case) shouldnot be confused with the minimum step for estimatingHa orHaM The radar radial resolution coincides with the verticalresolution only for antenna zenithal pointing (or elevationangle equal to 90) For low elevation angles such as thoseof scanning weather radars the vertical coordinatez inEq (9) is resolved at a variable range-dependent resolutionwhich in our case may be even less than few hundreds ofmeters For both eruption periods the estimated maximumheight is up to 10 km with a larger dynamical range ofvalues for the April event than for the May event It is worthnoting that the temporal trend ofHaM(t) is not necessarilycorrelated with the estimatedMa(t)

The maximum plume height retrievalsHaM provided byweather radars can be used as an input variable in mod-els that compute the Eruption Discharge Rate (EDR) a use-ful parameter to mark the intensity of a volcanic eruption(Wilson 1972 Sparks et al 1997) The thermal energy ofthe erupted tephra is used to heat the air trapped within theeruption jet and causes convective phenomena that raise theeruptive column When the EDR is known it is possibleto estimate the thickness of the ash layer that will settle onthe ground according to a model widely used for eruptioncolumns which produce strong plumes (Wilson et al 1978)Adapting the Morton relation to the Eyjafjoumlll volcano erup-tion (Morton et al 1952) and considering a basaltic magmathe estimated EDR indicated byQH(t) (m3 sminus1) can be ob-

22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]

Maximum plume height by VARR (Ca gt 10-6 kgm3) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]

Maximum plume height by VARR (Ca gt 10-6 kgm3) on May

1 Fig 5 Instantaneous maximum plume height versus scan days with input data from VARR algorithm with 2 concentration threshold (Cagt10-6 kgm3) In the upper panel the trend with reference to April time window 3 (since 0100 UTC on April 14 2010 till 2355 UTC on April 20 2010) in the lower panel the trend with 4 reference to May time window (since 0010 UTC on May 05 2010 till 2355 UTC on May 10 2010) 5

6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]

Maximum plume height by VARR (ZH

gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May

7 Fig 6 Instantaneous maximum plume height versus scan days with input data from VARR algorithm with 8 reflectivity threshold (ZHgt-6 dBZ) In the upper panel the trend with reference to April time window (since 9 0100 UTC on April 14 2010 till 2355 UTC on April 20 2010) in the lower panel the trend with reference to 10 May time window (since 0010 UTC on May 05 2010 till 2355 UTC on May 10 2010) 11

Fig 5 Instantaneous maximum plume height versus scan dayswith input data from VARR algorithm with concentration thresh-old (Ca gt 10minus6 kg m3) In the upper panel the trend with refer-ence to April time window (since 0100 UTC on 14 April 2010 till2355 UTC on 20 April 2010) in the lower panel the trend withreference to May time window (since 0010 UTC on 5 May 2010till 2355 UTC on 10 May 2010)

22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May


Fig 6 Instantaneous maximum plume height versus scan dayswith input data from VARR algorithm with reflectivity thresh-old (ZH gt minus6 dBZ) In the upper panel the trend with referenceto April time window (since 0100 UTC on 14 April 2010 till2355 UTC on 20 April 2010) in the lower panel the trend withreference to May time window (since 0010 UTC on 5 May 2010till 2355 UTC on 10 May 2010)

tained from maximum plume height through the followingapproximate relation (Oddsson et al 2009 Marzano et al2011a)



23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]

Eruption discharge rate instantaneous trend on April by VARR

05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]

Eruption discharge rate instantaneous trend on May by VARR

1 Fig 7 Instantaneous discharge rate of eruption (EDR) obtained from the maximum plume height versus scan 2 number with input data from VARR algorithm with concentration threshold (Cagt10-6 kgm3) In the upper panel 3 the trend with reference to April time window (since 0100 UTC on April 14 2010 till 2355 UTC on April 20 4 2010) in the lower panel the trend with reference to May time window (since 0010 UTC on May 05 2010 till 5 2355 UTC on May 10 2010) Mean EDR values are also quoted in both panels 6

7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]

Instantaneous EDR trend by VARR on April

05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]

Instantaneous EDR trend by VARR on May

8 Fig 8 Same as in Fig 7 but for EDR derived from the estimated instantaneous ash volume 9

10

Fig 7 Instantaneous Eruption Discharge Rate (EDR) obtainedfrom the maximum plume height versus scan number with in-put data from VARR algorithm with concentration threshold (Cagt

10minus6 kg mminus3) In the upper panel the trend with reference to Apriltime window (since 0100 UTC on 14 April 2010 till 2355 UTC on20 April 2010) in the lower panel the trend with reference to Maytime window (since 0010 UTC on 5 May 2010 till 2355 UTC on10 May 2010) Mean EDR values are also quoted in both panels

QH(t) sim= 0085[HaM(t)]4 (11)

The Eq (11) shows that EDR is linked to the fourth powerof the height and so small fluctuations of the height causelarge variations of the EDR EDR temporal trends obtainedfrom VARR using Eq (11) with a threshold on ash concen-trationCa are shown for both April and May time windowsin Fig 7 The power-law dependence ofQH on the maxi-mum plume height tends to amplify the EDR peaks Thisfigure suggests that the larger EDR is on 14 April and across17 April with an isolated peak on 19 April 2010 The be-haviour on May is more uniform with some relative maximaon 5 and 6 May 2010

The EDR can be also directly evaluated from the temporaltrend of the estimated ash volumeVa(t) The radar-derivedEDR QV (t) (m3 sminus1) is evaluated through the ratio betweenthe temporal average instantaneous volume and the samplinginterval1t

QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)

whereti is the i-th time step within the sampling period1tswhereVa is assumed constant in order to obtain the approx-imation of QV (t) in Eq (12) Similarly to Fig 7 Fig 8shows the estimatedQV (t) using Eq (12) for both the Apriland May periods The temporal trend ofQV (t) is quite dif-ferent from that ofQH(t) shown in Fig 7 The reason of thisdifference may be attributed to the fact thatQH takes into ac-count only the ash cloud altitude whereasQV is related to

23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10

Fig 8 Same as in Fig 7 but for EDR derived from the estimatedinstantaneous ash volume

the erupted 3-D volume Indeed the estimate ofQV (t) isaffected by the observation geometrical limits which reducethe detectedVa(t) partially reconstructed through the VPRapproach The estimate of EDR through Eq (12) evidencesthat the strongest peak is around the end of 16 April 2010with EDR up to 4000 m3 sminus1 whereas the May event showspeaks less than 300 m3 sminus1 with a more intense activity on5 May 2010

32 Retrieval spatial maps

The deposited ash at ground during the whole event can beestimated from the retrieved ash fall rateRa(λ ϕ z t) Byperforming a VPR reconstruction as indicated before andindicating withRa(λ ϕ z = zs t) the ash fall rate at the sur-face heightzs the spatial distribution of the radar-deriveddeposited tephra density or loadingDa(λ ϕ) (kg mminus2) is ob-tained from

Da(λφ) equiv

tfintti

Ra(λφz = zst)dt (13)

whereti andtf are the initial and final time steps of the vol-canic eruption The total space-time deposited tephra massMaT (kg) from radar measurements can be evaluated by us-ing

MaT=

intDageDmin

Da(λφ)dS (14)

whereDmin is a threshold value ofDa The radar-derivedtotal ash volume may be estimated byVaT= MaTρa In orderto convert the deposited ash loadingDa into deposited ashdepthda (m) it holdsda = Daρa Note thatMaT could beestimated by integrating Eq (8) as well but in that case noVPR reconstruction would be performed



24

1 Fig 9 Distal fallout spatial maps retrieved by VARR The distributions show the accumulated ash mass at the 2 ground every twelve hours (from left to right from top panel to bottom) since 0000 UTC on April 15 2010 till 3 2355 UTC on April 18 2010 The black edged triangle is centred in the exact position of the Eyjafjoumlll volcano 4 whereas colorbars are scaled to match the different dynamic range of the distributions 5

6

Fig 9 Distal fallout spatial maps retrieved by VARR The distri-butions show the accumulated ash mass at the ground every twelvehours (from left to right from top panel to bottom) since 0000 UTCon 15 April 2010 till 2355 UTC on 18 April 2010 The black edgedtriangle is centred in the exact position of the Eyjafjoumlll volcanowhereas colorbars are scaled to match the different dynamic rangeof the distributions

Deposited ash massDa(xy) evaluated through Eq (12)in terms of distal spatial maps derived from radar can be anappealing way to monitor the evolution of a volcanic eruptionin terms of ash fallout as shown in Fig 9 and Fig 10 Thefigures show the accumulated ground mass distribution of theash within geo-referenced spatial maps thus providing a use-ful instrument to gather information about the time progres-sion of the ash fallout These results indicate that the Aprilvolcanic eruption ejected a bigger amount of tephra than thatdue to the May volcanic eruption In order to quantitativelyconfirm previous considerations Tables 2 and 3 show the to-tal ash mass and total volume values for the 14ndash20 April 2010and and the 5ndash10 May 2010 eruption period respectively ob-tained from radar-derived ashfall rateRa by selecting a fallvelocity valuesav andbv derived from the Harris and Rose(1983) ash fallout (HAF) data and the Wilson (1972) ash fall-out (WAF) data Sensitivity of total mass volume to the stan-dard deviation of estimated ashfall rate is also shown

25

1 Fig 10 Distal fallout spatial maps retrieved by VARR The distributions show the accumulated ash mass at the 2 ground every twelve hours (from left to right from top panel to bottom) since 0000 UTC on May 05 2010 till 3 2355 UTC on May 08 2010 The black edged triangle is centred in the exact position of the Eyjafjoumlll volcano 4 whereas colorbars are scaled to match the different dynamic range of the distributions 5

6

Fig 10 Distal fallout spatial maps retrieved by VARR The distri-butions show the accumulated ash mass at the ground every twelvehours (from left to right from top panel to bottom) since 0000 UTCon 5 May 2010 till 2355 UTC on 8 May 2010 The black edgedtriangle is centred in the exact position of the Eyjafjoumlll volcanowhereas colorbars are scaled to match the different dynamic rangeof the distributions

The sensitivity to the ash category is quite relevant in theradar mass estimation The latter consideration is confirmedby Figs 11 and 12 which respectively show the histogramof the 9 radar-estimated ash categories by VARR ash clas-sification (see Table 1) during the whole eruption event andthe occurrence of a given ash concentration (small moderateand intense) within each ash class (fine ash coarse ash andlapilli) With reference to the whole eruption the total num-ber of available resolution volumes was 6 200 376 for Apriland 5 340 244 for May but they have been reduced respec-tively to 121 442 and 30 423 considering only ash-containingvolumes (ie excluding all resolution volumes with ash classlabel value equal to 0) The figures respectively show thatwith reference to April almost 62 of detected ash belongsto coarse ash with moderate concentration (c = 5) whereasno bins were labeled as fine ash with small concentration(c = 1) nor lapilli with intense concentration (c = 9) For



the observations in May above the 85 of total detected ashbelongs to coarse ash with small and moderate concentration(c = 4 andc = 5) whereas there is a low occurence of lapilli(limited to small concentration withc = 7)

26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]

Dataset of April 2010

000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]

Small Moderate Intense000

2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500

10000 Dataset of May 2010

000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration

1 Fig 11 Histograms showing the probability of a given ash concentration value with respect to the total number 2 of labels attached to the processed unit radar volumes (121442 for April and 30423 for May) and to the ash class 3 The latter are displayed on panels from top to bottom as fine ash coarse ash and lapilli Only significant volumes 4 have been considered with reference to the whole eruption since 0100 UTC on April 14 2010 till 2355 UTC 5 on April 20 2010 (left panels) and since 0010 UTC on May 5 2010 till 2355 UTC on May 10 2010 (right 6 panels) Note that very few lapilli were detected during the eruptions 7

1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]

Dataset from 0100 UTC on April 14 2010 till 2355 UTC on April 20 2010

1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]

Dataset from 0010 UTC on May 5 2010 till 2355 UTC on May 10 2010

8 Fig 12 Histogram showing the probability of a given ash class label value with respect to the total number of 9 labels attached to the processed unit radar volumes (121442 for April and 30423 for May) Only significant 10 volumes have been considered with reference to the whole eruption since 0100 UTC on April 14 2010 till 11 2355 UTC on April 20 2010 and since 0010 UTC on May 5 2010 till 2355 UTC on May 10 2010 Both on 12 April and May higher occurrence corresponds to coarse ash with moderate concentration whereas lapilli and 13 fine ash with small concentration have been virtually not observed during the eruption 14

Fig 11Histograms showing the probability of a given ash concen-tration value with respect to the total number of labels attached tothe processed unit radar volumes (121 442 for April and 30 423 forMay) and to the ash class The latter are displayed on panels fromtop to bottom as fine ash coarse ash and lapilli Only significantvolumes have been considered with reference to the whole eruptionsince 0100 UTC on 14 April 2010 till 2355 UTC on 20 April 2010(left panels) and since 0010 UTC on 5 May 2010 till 2355 UTC on10 May 2010 (right panels) Note that very few lapilli were detectedduring the eruptions

Coarse ash particles as expected are the most probablewith a lower occurrence of finer particles around the volcaniccaldera (except fine ash with small concentration) On thecontrary lapilli are found in regions closer to the volcanicvent due to ballistic ejections (note that both on April andMay virtually no lapilli have been detected) The occurrencesare quite similar in both time windows as shown in Fig 11coarse ash with small concentration percentage occurrence ishigher on May whereas the fine ash distribution with respectto ash concentration is very similar Lapilli occurrence isvery low on both eruptions There are two reasons to explainthe difference in the total number of ash containing volumesbetween April and May dataset First of all the April datarefer to one week whereas the May ones are provided withreference to six days moreover the May eruption has beenless powerful than the peak of the volcanic activity reachedduring the month of April and so the number of volumes isnot a simple scaling between the two cases of study

26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]



Fig 12 Histogram showing the probability of a given ash classlabel value with respect to the total number of labels attached tothe processed unit radar volumes (121 442 for April and 30 423 forMay) Only significant volumes have been considered with refer-ence to the whole eruption since 0100 UTC on 14 April 2010 till2355 UTC on 20 April 2010 and since 0010 UTC on 5 May 2010till 2355 UTC on 10 May 2010 Both on April and May higheroccurrence corresponds to coarse ash with moderate concentrationwhereas lapilli and fine ash with small concentration have been vir-tually not observed during the eruption

4 Conclusions

The Eyjafjoumlll explosive volcanic eruptions occurred on Apriland May 2010 have been analyzed and quantitatively inter-preted by using ground-based weather radar data and VARRinversion technique The latter has been applied to the Ke-flaviacutek C-band weather radar located at a distance of about155 km from the volcano vent The VARR methodology hasbeen summarized and applied to available radar time seriesto estimate the plume maximum height ash particle categoryash volume ash fallout and ash concentration every five min-utes Estimates of the discharge rate of eruption based on theretrieved ash plume top height have been also provided to-gether with the deposited ash at ground

The possibility of monitoring 24 h a day in all weatherconditions at a fairly high spatial resolution and every fewminutes after the eruption is the major advantage of usingground-based microwave radar systems The latter can becrucial systems to monitor the ldquonear-sourcerdquo eruption fromits early-stage near the volcano vent dominated by coarse



Table 2 Total mass and total volume values for the 14ndash20 April 2010 eruption period obtained from radar-derived ashfall rateRa byselecting a fall velocity valuesav andbv derived from the Harris and Rose (1983) ash fallout (HAF) data and the Wilson (1972) ash fallout(WAF) data Sensitivity of total mass volume to the standard deviation of estimated ashfall rate indicated byσ(Ra) is also shown

Source Fallout model Total mass (kg) Total volume (m3)

VARR usingRaminusσ(Ra) HAF 82455times 1010 68713times 107

VARR usingRa HAF 85193times 1010 70994times 107

VARR usingRa+σ(Ra) HAF 87734times 1010 73112times 107

VARR usingRaminusσ(Ra) WAF 67303times 1010 56086times 107

VARR usingRa WAF 70193times 1010 58494times 107

VARR usingRa+σ(Ra) WAF 63656times 1010 53046times 107

Table 3 Same as in Table 2 but for the 5ndash10 May 2010 eruption period








ash and blocks to ash-dispersion stage up to hundreds ofkilometers dominated by transport and evolution of coarseand fine ash particles For distances larger than about sev-eral tens of kilometers fine ash might become ldquoinvisiblerdquo tothe radar In this respect radar observations can be comple-mentary to satellite lidar and aircraft observations More-over radar-based products can be used to initialize dispersionmodel inputs Due to logistics and space-time variability ofthe volcanic eruptions a suggested optimal radar system todetect ash cloud could be a portable X-band weather Dopplerpolarimetric radar (Marzano et al 2011b) This radar systemmay satisfy technological economical and new scientific re-quirements to detect ash cloud The sitting of the observationsystem which is a problematic tradeoff for a fixed radar sys-tem (as the volcano itself may cause a beam obstruction andthe ash plume may move in unknown directions) can be eas-ily solved by resorting to portable systems

Further work is needed to assess the VARR potential usingexperimental campaign data Future investigations should bedevoted to the analysis of the impact of ash aggregates onmicrowave radar reflectivity and on the validation of radarestimates of ash amount with ground measurements whereavailable The last task is not an easy one as the ash fallis dominated by wind advection and by several complicatedmicrophysical processes This means that what is retrievedwithin an ash cloud may be not representative of what wascollected at ground level in a given area Spatial integrationof ground-collected and radar-retrieved ash amounts may be

considered to carry out a meaningful comparison Prelimi-nary results for the Griacutemsvoumltn case study show that the radar-based tephra ash mass estimates retrievals compare well withthe deposited ash blanket estimated from in situ ground sam-pling within the volcanic surrounding area (Marzano et al2011a)

AcknowledgementsWe are very grateful to B Paacutelmason H Peacute-tursson and S Karlsdoacutettir (IMO Iceland) for providing C-bandradar data and useful suggestions on data processing The con-tribution and stimulus of B De Bernardinis (ISPRA Italy andformerly DPC Italy) and G Vulpiani (DPC Italy) is gratefullyacknowledged We also wish to thank S Pavone and S Barbieri(Sapienza University Italy) who contributed to the development ofthe VARR software and the comparison analysis This work hasbeen partially funded by the Italian Department of Civil Protection(DPC Rome Italy) under the project IDRA and by the SapienzaUniversity of Rome (Italy)

Edited by F Prata

References

Ansmann A Tesche M Gro S Freudenthaler V Seifert PHiebsch A Schmidt J Wandinger U Mattis I Muumlller Dand Wiegner M The 16 april 2010 major volcanic ash plumeover central Europe EARLINET lidar and AERONET photome-ter observations at Leipzig and Munich Germany Geophys ResLett L13810doi1010292010GL043809 2010



Bennett A J Odams P Edwards D and Arason THORN Monitoringof lightning from the AprilndashMay 2010 Eyjafjallajoumlkull volcaniceruption using a very low frequency lightning location networkEnviron Res Lett 5 44013ndash44022 2010

Bonadonna C Phillips J C and Houghton B F Modelingtephra sedimentation from a Ruapehu weak plume eruption JGeophys Res 110 B08209doi1010292004JB003515 2005

Costa A Macedonio Gand Folch A A three dimensional Eule-rian model for transport and deposition of volcanic ashes EarthPlanet Sci Lett 241 634ndash647 2006

Duggen S Olgun N Croot P Hoffmann L Dietze HDelmelle P and Teschner C The role of airborne volcanicash for the surface ocean biogeochemical iron-cycle a reviewBiogeosciences 7 827ndash844doi105194bg-7-827-2010 2010

Durant A J Bonadonna C and Horwell C J Atmosphericand environmental impacts of volcanic particulates Elements 6235ndash240 2010

Flentje H Claude H Elste T Gilge S Koumlhler U Plass-Duumllmer C Steinbrecht W Thomas W Werner A andFricke W The Eyjafjallajoumlkull eruption in April 2010U- detec-tion of volcanic plume using in-situ measurements ozone sondesand lidar-ceilometer profiles Atmos Chem Phys 10 10085ndash10092doi105194acp-10-10085-2010 2010

Gangale G Prata A J and Clarisse L The infrared spectralsignature of volcanic ash determined from high-spectral reso-lution satellite measurements Remote Sens Environ 114(2)414ndash425 2010

Gasteiger J Groszlig S Freudenthaler V and Wiegner M Vol-canic ash from Iceland over Munich mass concentration re-trieved from ground-based remote sensing measurements At-mos Chem Phys 11 2209ndash2223doi105194acp-11-2209-2011 2011

Gertisser R Eyjafjallajoumlkull volcano causes widespread disruptionto European air traffic Geol Today 26 94ndash95 2010

Gouhier M and Donnadieu F Mass estimations of ejectafrom Strombolian explosions by inversion of Dopplerradar measurements J Geophys Res 113 B10202doi1010292007JB005383 2008

Graf H-F Herzog M Oberhuber J M and Textor C Effectof environmental conditions on volcanic plume rise J GeophysRes 104 20 24309ndash24320 1999

Guethmundsson M T Pedersen R Vogfjoumlreth K ThorbjarnardoacutettirB Jakobsdoacutettir S and Roberts M J Eruptions of Eyjafjalla-joumlkull Volcano Iceland EOS 91 190ndash191 2010

Harris D M and Rose W I Estimating particle sizes concen-trations and total mass of ash in volcanic clouds using weatherradar J Geophys Res 88 10969ndash10983 1983

Kahn R A Li W-H Moroney C Diner D J Martonchik JV and Fishbein E Aerosol source plume physical characteris-tics from space-based multiangle imaging J Geophys Res 112D11205doi1010292006JD007647 2007

Lacasse C Karlsdoacutettir S Larsen G Soosalu H Rose W Iand Ernst G G J Weather radar observations of the Hekla 2000eruption cloud Iceland Bull Volcanol 66 457ndash473 2004

Larsen G Guethdmundsson M T and Bjoumlrnsson H Eight cen-turies of periodic volcanism at the center of the Iceland hotspotrevealed by glacier tephrostratigraphy Geology 26(10) 943ndash946 1998

Madonna F Amodeo A DrsquoAmico G Mona L and Pap-

palardo G Observation of non-spherical ultragiant aerosolusing a microwave radar Geophys Res Lett 37 L21814doi1010292010GL044999 2010

Marzano F S Picciotti E and Vulpiani G Rain field and reflec-tivity vertical profile reconstruction from C-band radar volumet-ric data IEEE T Geosci Remote 42(4) 1033ndash1046 2004

Marzano F S Vulpiani G and Rose W I Microphysical char-acterization of microwave radar reflectivity due to volcanic ashclouds IEEE T Geosci Remote 44 313ndash327 2006a

Marzano F S Barbieri S Vulpiani G and Rose W I Volcanicash cloud retrieval by ground-based microwave weather radarIEEE T Geosci Remote 44 3235ndash3246 2006b

Marzano F S Marchiotto S Barbieri S Textor C and Schnei-der D Model-based weather radar remote sensing of explosivevolcanic ash eruption IEEE T Geosci Remote 48 3591ndash36072010a

Marzano F S Barbieri S Picciotti E and Karlsdoacutettir S Mon-itoring subglacial volcanic eruption using ground-based C-bandradar imagery IEEE T Geosci Remote 48 403ndash414 2010b

Marzano F S Lamantea M Montopoli M Oddsson B andGuethmundsson M T Validating subglacial volcanic eruptionusing ground-based C-band radar imagery IEEE T Geosci Re-mote in press 2011a

Marzano F S Picciotti E Montopoli M and Vulpiani GSynthetic signatures of volcanic ash cloud particles from X-band dual-polarization radar IEEE T Geosci Remote 99 1ndash192011b

McCarthy E B Bluth G J S Watson I M and Tupper ADetection and analysis of the volcanic clouds associated with the18 and 28 August 2000 eruptions of Miyakejima volcano JapInt J Remote Sens 29(22) 6597ndash6620 2008

Mona L Amodeo A Boselli A Cornacchia C DrsquoAmico GGiunta A Madonna F and Pappalardo G Observations ofthe Eyjafjallajoumlkull eruptionrsquos plume at Potenza EARLINET sta-tion Geophys Res Abs 12 EGU2010 15747 2010

Morton B R Geoffrey Taylor F R S and Turner J Turbu-lent gravitational convection from maintained and instantaneoussources Proceedings of the Royal Society of London Series AMathematical and Physical Sciences A234 1ndash23 1956

Oddsson B Guethdmundsson M T Larsen G and KarlsdoacutettirS Griacutemsvoumltn 2004 Weather radar records and plume transportmodels applied to a phreatomagmatic basaltic eruption ProcIAVCEI (International Association of Volcanology and Chem-istry of the Earthrsquos Interior 2008 Reykjaviacutek (Iceland) 18ndash24 Au-gust 2008

Pavolonis M J Wayne F F Heidinger A K and Gallina G MA daytime complement to the reverse absorption technique forimproved automated detection of volcanic ash J Atmos OceaTechnol 23 1422ndash1444 2006

Pedersen R and Sigmundsson F Temporal development ofthe 1999 intrusive episode in the Eyjafjallajoumlkull volcano Ice-land derived from InSAR images Bull Volcanol 68 377ndash393doi101007s00445-005-0020-y 2006

Petersen G N A short meteorological overview of the Eyjafjal-lajoumlkull eruption 14 Aprilndash23 May 2010 Weather 65 203ndash2072010

Pietruczuk A Krzyscin J W Jaroslawski J Podgorski J PSobolewski and Wink J Eyjafjallajoumlkull volcano ash observedover Belsk (52 N 21 E) Poland in April 2010 Int J Remote



Sens 31 3981ndash3986 2010Prata A J and Tupper A Aviation hazards from volcanoes the

state of the science Nat Hazards 51 239ndash244 2009Robock A Volcanic eruptions and climate Rev Geophys 38

191ndash219 2000Rose W J and Durant A J Fine ash content of explosive erup-

tions J Volcanol Geoth Res 186 32ndash39 2009Sauvageot H Radar meteorology Artech House Boston (MA)

1992Schumann U Weinzierl B Reitebuch O Schlager H Minikin

A Forster C Baumann R Sailer T Graf K Mannstein HVoigt C Rahm S Simmet R Scheibe M Lichtenstern MStock P Ruumlba H Schaumluble D Tafferner A Rautenhaus MGerz T Ziereis H Krautstrunk M Mallaun C Gayet J-F Lieke K Kandler K Ebert M Weinbruch S Stohl AGasteiger J GroSS S Freudenthaler V Wiegner M Ans-mann A Tesche M Olafsson H and Sturm K Airborne ob-servations of the Eyjafjalla volcano ash cloud over Europe duringair space closure in April and May 2010 Atmos Chem Phys11 2245ndash2279doi105194acp-11-2245-2011 2011

Sparks R The dimensions and dynamics of volcanic eruptioncolumns Bull Volcanol 48 3ndash15 1986

Sparks R S J Bursik M I Carey S N Gilbert J S Glaze LSigurdsson H and Woods A W Volcanic Plumes New YorkWiley 1997

Stohl A Hittenberger M and Wotawa G Validation of theLagrangian particle dispersion model FLEXPART against largescale tracer experiment data Atmos Environ 32 4245ndash42641998

Stohl A Prata A J Eckhardt S Clarisse L Durant A HenneS Kristiansen N I Minikin A Schumann U Seibert PStebel K Thomas H E Thorsteinsson T Toslashrseth K andWeinzierl B Determination of time- and height-resolved vol-canic ash emissions and their use for quantitative ash disper-sion modeling the 2010 Eyjafjallajoumlkull eruption Atmos ChemPhys 11 4333ndash4351doi105194acp-11-4333-2011 2011

Thordarson T and Larsen G Volcanism in Iceland in historicaltime Volcano types eruption styles and eruptive history J Geo-dynamics 43(1) 118ndash152 2007

Yu T Rose W I and Prata A J Atmospheric correction forsatellite based volcanic ash mapping and retrievals using split-window IR data from GOES and AVHRR J Geophys Res107(D16) 4311doi1010292001JD000706 2002

Wen S and Rose W I Retrieval of sizes and total masses of parti-cles in volcanic clouds using AVHRR bands 4 and 5 J GeophysRes 99 5421ndash5431 1994

Wilson L Explosive volcanic eruptions ndash Part II The atmospherictrajectories of pyroclasts Geophys J R Astron Soc 30(2)381ndash392 1972

Wilson L Sparks R S J Huang T C and Watkins N D Thecontrol of volcanic column heights by eruption energetics anddynamics J Geophys Res 83(83) 1829ndash1836 1978

Zehner C Editor Monitoring Volcanic Ash from Space Pro-ceedings of the ESA-EUMETSAT workshop on the 14 April to23 May 2010 eruption at the Eyjafjoll volcano South IcelandFrascati Italy ESA-Publication STM-280doi105270atmch-10-01 26ndash27 May 2010



protection and air traffic management needs not only a de-tection of the erupted and dispersed ash cloud but also theestimation and forecast of its ash content (Prata and Tup-per 2009) The Eyjafjoumlll eruption on 2010 has been oneof the best documented European volcanic events in termsof ground and satellite observations (eg Ansmann et al2010 Bennet et al 2010 Flentje et al 2010 Gasteiger etal 2011 Guethmundsson et al 2010 Madonna et al 2010Mona et al 2010 Schumann et al 2011 Pietruczuk et al2010 Stohl et al 2011) Particular importance is devoted tothe ldquonear-sourcerdquo (where the ldquosourcerdquo is the volcano vent)instrumentation as measured data can be used to properlyinitialized ash-plume dispersion models (eg Bonadonna etal 2009 Costa et al 2006 Stohl et al 1998) Coarse ashand lapilli are expected to fall within few hours from ejec-tion time into air and within distances less than few hun-dreds of kilometres from the volcanic vent (Rose and Du-rant 2009) This deposited tephra (ie the fragmental ma-terial produced by a volcanic eruption) is typically estimatedto be more than 99 of the total ash mass (Wen and Rose1994) Advanced volcanic sites can deal with an ensem-ble of ldquonear-sourcerdquo synergetic instruments (Sparks et al1997 Zehner 2010) in situ drillings and sondes surveil-lance flights for plume monitoring GNSS (Global Naviga-tion Satellite System) differential receivers for deformationmeasurements seismic signal receivers for tremor analysisinterferometric synthetic aperture radars (InSARs) for de-formation imaging ground-based lidars ceilometers pho-tometers and microwave radars for plume probing very-low-frequency (VLF) receivers for lightning detection and satel-lite infrared radiometers for broadscale plume tracking EvenUnmanned airborne vehicles (UAVs) cannot be used to probethe near-source tephra due to inherent risks (Schumann et al2011) Satellite visible and thermal infrared split-windowtechniques may miss ldquonear-sourcerdquo tephra as they are basi-cally insensitive to ash particles larger than few tens of mi-crons (Yu et al 2002 Pavolonis et al 2006 Kahn et al2007 McCarthy et al 2008 Stohl et al 2010) On the otherhand ground-based optical ldquonear-sourcerdquo observations maybe completely opaque due to the strong extinction of coarseand large ash particles (Zehner 2010)

ldquoNear-sourcerdquo observations if available do not gener-ally include estimates on the ash plume volume and concen-tration The magma discharge estimate is primarily basedon an empirical relationship established between observederuption column heights derived from ground-based weatherradars and magma discharge (Lacasse et al 2004 Odds-son et al 2009) Estimates on concentration of ash solidmaterial in the eruption plume are usually based on theoret-ical assumptions which may be supported by satellite-basedobservations of the ash cloud at mid to far distances (hun-dreds of kilometres) from the vent (Wilson 1972 Sparkset al 1997) In this context active microwave remote sens-ing through ground-based scanning weather radars can bebetter exploited and can represent a very powerful and to

some extent unique instrument to study explosive eruptionsin proximity of volcanic vents (Harris and Rose 1983 La-casse et al 2004 Marzano et al 2006a Gouhier and Don-nadieu 2008) In the ldquonear-sourcerdquo region weather radarsmay be capable to provide in principle not only the plumeheight but also ash particle category ash volume ash fall-out and ash concentration (Marzano et al 2006b 2010b2011a) Conventional weather radar targets are precipitatinghydrometeors whose shape dimension and dielectric proper-ties are undoubtedly different from tephra ones (Sauvageot1992) This implies that weather radars cannot be used forash cloud monitoring without developing ad hoc inversionmethodologies and techniques to process radar data streamAmong these algorithms the VARR (Volcanic Ash RadarRetrieval) approach has been shown to be a relatively generaltheoretical and operational framework to infer in a quantita-tive way ash mass category concentration and fallout ratefrom three-dimensional (3-D) scanning weather-radar mea-surements (Marzano et al 2006b 2010a) The VARR prod-ucts must be carefully treated as any remote sensing inver-sion methodology they are obtained under proper physical-statistical assumptions and given sensor limitations (eg re-ceiver sensitivity and polarization agility)

The potential of VARR data processing in observing vol-canic ash clouds has been analyzed using some case studieswhere volcano eruptions happened near an available weatherradar (i) the Griacutemsvoumltn volcano eruption in 2004 analyzedtogether with the Icelandic Meteorological Office (IMO) us-ing a C-band weather radar (Marzano et al 2006b 2010a2010b) (ii) the Augustine volcano eruption in 2006 ana-lyzed together with the US Geological Survey Alaska Vol-cano Observatory using an S-band weather radar (Marzanoet al 2010b) This work presents new results of the VARRmethodology applied to the sub-glacial explosive eruptionsof Icelandic Eyjafjoumlll stratovolcano whose maximum activ-ities occurred on April and May 2010 The 2010 eruptionshave been monitored and measured by the Keflaviacutek C-bandweather radar at a distance of about 155 km from the vol-cano vent (Guethmundsson et al 2010) The distance be-tween the Eyjafjoumlll volcano and the Icelandic coast is ap-proximately 20 km Due to the proximity between the vol-cano and the Atlantic Ocean and the prevailing northerlywinds which stretched the plume toward the mainland Eu-rope collecting ground data samples in order to estimate thetotal ejected tephra or the ash distribution is not an easy taskespecially in the nearby of the Eyjafjoumlll volcano In this re-spect weather radar is one of the most powerful instrumentsto investigate this phenomenon and estimate the near-sourceash fallout

This paper is structured as follows In Sect 2 the Ey-jafjoumlll eruptions of April and May 2010 are described andthe effects of the volcanic plume are summarized Moreoverradar data are discussed and VARR algorithm data process-ing features are briefly introduced In Sect 3 weather radarretrievals with reference to time and spatial volcanic cloud















ZH(rθϕ) =λ4


D2intD1

D6NaX(D)dD = m6 (1)











19

1

2

3





20

1

2

3










c(rθϕ) = Minc


2(σ

(c)Z

)2+ ln

(σ

(c)Z


(2)




(c)Z )




Ra=

D2intD1

va(D)ma(D)NaX(D)dD

Ca=

D2intD1

ma(D)NaX(D)dD

(3)





(c)a (rθϕ) = ccZ

dc

Hm(rθϕ)

C(c)a (rθϕ) = acZ

bc

Hm(rθϕ)

(4)














ϕ =180

π

[asin

(sin(ϕR)cos

(r

Re

))+cos(ϕR)sin

(r

Re

)cos(φ)

](5)

λ =180

π

[λR

180

π+atan2

(sin(φ)sin

(r

Re

)cos(ϕR)cos

(r

Re



z =

radicr2+R2





Va(t) equiv

intCa(λφzt)geCath

dV (7)





21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14




Ma(t) equiv

intVa(t)




21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14





Ha(λφt) equiv


(9)









22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May



22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May






23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10



QH(t) sim= 0085[HaM(t)]4 (11)



QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)


23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10





Da(λφ) equiv

tfintti



MaT=

intDageDmin

Da(λφ)dS (14)




24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References





































































ZH(rθϕ) =λ4


D2intD1

D6NaX(D)dD = m6 (1)











19

1

2

3





20

1

2

3










c(rθϕ) = Minc


2(σ

(c)Z

)2+ ln

(σ

(c)Z


(2)




(c)Z )




Ra=

D2intD1

va(D)ma(D)NaX(D)dD

Ca=

D2intD1

ma(D)NaX(D)dD

(3)





(c)a (rθϕ) = ccZ

dc

Hm(rθϕ)

C(c)a (rθϕ) = acZ

bc

Hm(rθϕ)

(4)














ϕ =180

π

[asin

(sin(ϕR)cos

(r

Re

))+cos(ϕR)sin

(r

Re

)cos(φ)

](5)

λ =180

π

[λR

180

π+atan2

(sin(φ)sin

(r

Re

)cos(ϕR)cos

(r

Re



z =

radicr2+R2





Va(t) equiv

intCa(λφzt)geCath

dV (7)





21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14




Ma(t) equiv

intVa(t)




21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14





Ha(λφt) equiv


(9)









22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May



22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May






23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10



QH(t) sim= 0085[HaM(t)]4 (11)



QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)


23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10





Da(λφ) equiv

tfintti



MaT=

intDageDmin

Da(λφ)dS (14)




24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References

























































19

1

2

3





20

1

2

3










c(rθϕ) = Minc


2(σ

(c)Z

)2+ ln

(σ

(c)Z


(2)




(c)Z )




Ra=

D2intD1

va(D)ma(D)NaX(D)dD

Ca=

D2intD1

ma(D)NaX(D)dD

(3)





(c)a (rθϕ) = ccZ

dc

Hm(rθϕ)

C(c)a (rθϕ) = acZ

bc

Hm(rθϕ)

(4)














ϕ =180

π

[asin

(sin(ϕR)cos

(r

Re

))+cos(ϕR)sin

(r

Re

)cos(φ)

](5)

λ =180

π

[λR

180

π+atan2

(sin(φ)sin

(r

Re

)cos(ϕR)cos

(r

Re



z =

radicr2+R2





Va(t) equiv

intCa(λφzt)geCath

dV (7)





21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14




Ma(t) equiv

intVa(t)




21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14





Ha(λφt) equiv


(9)









22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May



22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May






23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10



QH(t) sim= 0085[HaM(t)]4 (11)



QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)


23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10





Da(λφ) equiv

tfintti



MaT=

intDageDmin

Da(λφ)dS (14)




24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References

























































20

1

2

3










c(rθϕ) = Minc


2(σ

(c)Z

)2+ ln

(σ

(c)Z


(2)




(c)Z )




Ra=

D2intD1

va(D)ma(D)NaX(D)dD

Ca=

D2intD1

ma(D)NaX(D)dD

(3)





(c)a (rθϕ) = ccZ

dc

Hm(rθϕ)

C(c)a (rθϕ) = acZ

bc

Hm(rθϕ)

(4)














ϕ =180

π

[asin

(sin(ϕR)cos

(r

Re

))+cos(ϕR)sin

(r

Re

)cos(φ)

](5)

λ =180

π

[λR

180

π+atan2

(sin(φ)sin

(r

Re

)cos(ϕR)cos

(r

Re



z =

radicr2+R2





Va(t) equiv

intCa(λφzt)geCath

dV (7)





21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14




Ma(t) equiv

intVa(t)




21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14





Ha(λφt) equiv


(9)









22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May



22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May






23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10



QH(t) sim= 0085[HaM(t)]4 (11)



QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)


23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10





Da(λφ) equiv

tfintti



MaT=

intDageDmin

Da(λφ)dS (14)




24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References






























































c(rθϕ) = Minc


2(σ

(c)Z

)2+ ln

(σ

(c)Z


(2)




(c)Z )




Ra=

D2intD1

va(D)ma(D)NaX(D)dD

Ca=

D2intD1

ma(D)NaX(D)dD

(3)





(c)a (rθϕ) = ccZ

dc

Hm(rθϕ)

C(c)a (rθϕ) = acZ

bc

Hm(rθϕ)

(4)














ϕ =180

π

[asin

(sin(ϕR)cos

(r

Re

))+cos(ϕR)sin

(r

Re

)cos(φ)

](5)

λ =180

π

[λR

180

π+atan2

(sin(φ)sin

(r

Re

)cos(ϕR)cos

(r

Re



z =

radicr2+R2





Va(t) equiv

intCa(λφzt)geCath

dV (7)





21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14




Ma(t) equiv

intVa(t)




21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14





Ha(λφt) equiv


(9)









22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May



22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May






23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10



QH(t) sim= 0085[HaM(t)]4 (11)



QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)


23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10





Da(λφ) equiv

tfintti



MaT=

intDageDmin

Da(λφ)dS (14)




24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References































































ϕ =180

π

[asin

(sin(ϕR)cos

(r

Re

))+cos(ϕR)sin

(r

Re

)cos(φ)

](5)

λ =180

π

[λR

180

π+atan2

(sin(φ)sin

(r

Re

)cos(ϕR)cos

(r

Re



z =

radicr2+R2





Va(t) equiv

intCa(λφzt)geCath

dV (7)





21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14




Ma(t) equiv

intVa(t)




21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14





Ha(λφt) equiv


(9)









22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May



22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May






23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10



QH(t) sim= 0085[HaM(t)]4 (11)



QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)


23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10





Da(λφ) equiv

tfintti



MaT=

intDageDmin

Da(λφ)dS (14)




24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References

























































21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14




Ma(t) equiv

intVa(t)




21

14 15 16 17 18 19 200

5

10

15x 10

8

Inst

an

tan

eo

us

ma

ss [m

3 ]


05 06 07 08 09 100

5

10

15x 10

7

Inst

an

tan

eo

us

ma

ss [m

3 ]



8

14 15 16 17 18 19 200

5

10

x 105

Inst

an

tan

eo

us

volu

me

[m3 ]


05 06 07 08 09 100

5

10

x 104

Inst

an

tan

eo

us

volu

me

[m3 ]



14





Ha(λφt) equiv


(9)









22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May



22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May






23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10



QH(t) sim= 0085[HaM(t)]4 (11)



QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)


23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10





Da(λφ) equiv

tfintti



MaT=

intDageDmin

Da(λφ)dS (14)




24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References




























































22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May



22

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]



6

14 15 16 17 18 19 200

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on April

05 06 07 08 09 100

5

10

Ma

x p

lum

e h

eig

ht [

km]


gt -6 dBZ) on May






23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10



QH(t) sim= 0085[HaM(t)]4 (11)



QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)


23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10





Da(λφ) equiv

tfintti



MaT=

intDageDmin

Da(λφ)dS (14)




24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References

























































23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10



QH(t) sim= 0085[HaM(t)]4 (11)



QV (t) =Va(t)

1t=

1

1t

1

1t

1tint0

Va(t)dt

sim=Va(ti)

1ts(12)


23

14 15 16 17 18 19 200

200

400

600

800

1000

ED

R [m

3 s]


05 06 07 08 09 100

200

400

600

800

1000

ED

R [m

3 s]



7

14 15 16 17 18 19 200

1000

2000

3000

4000

Inst

an

tan

eo

us

ED

R [m

3 s]


05 06 07 08 09 100

100

200

300

400

Inst

an

tan

eo

us

ED

R [m

3 s]



10





Da(λφ) equiv

tfintti



MaT=

intDageDmin

Da(λφ)dS (14)




24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References

























































24


6



25


6






26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References


























































26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]





26

000

2500

5000

7500

10000

Fin

e as

hpr

obab

ility

[

]


000

2500

5000

7500

10000

Coa

rse

ash

prob

abili

ty [

]


2500

5000

7500

10000

Concentration

Lapi

llipr

obab

ility

[

]

000

2500

5000

7500


000

2500

5000

7500

10000


2500

5000

7500

10000

Concentration


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Pro

babi

lity

[]


1 2 3 4 5 6 7 8 9000

2500

5000

7500

10000

Ash class label []

Pro

babi

lity

[]




4 Conclusions

























Edited by F Prata

References













































































Edited by F Prata

References
























































the eyjafjöll explosive volcanic eruption from a microwave weather radar … · 2015-01-31 ·...

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