JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. B4, PAGES 6513-6533, APRIL 10, 2001
Reconstruction of eruption column dynamics on the
basis of grain size of tephra fall deposits
2. Application to the Pinatubo 1991 eruption
TakehiroKoyaguchiand MarekazuOhno1
Department of Complexity Scienceand Engineering,Graduate Schoolof Frontier Sciences
University of Tokyo, Tokyo, Japan
Abstract. The granulometricmethods to reconstructeruption column dynamics
developedin paper I are applied to the tephra fall depositsof the climactic Plinian
phaseof the 1991 eruption at Pinatubo. The tephra fall depositsare composedof
two units: layer C1, which correspondsto the first half of the climactic phase,and
layer C: the secondhall The granulometricestimatesof the expansionrate of the
umbrella
cloudfor layersC1 andC: are7 x 1010and3 x 1010m3/s,respectively,
which agreewith the observationsof satellite images. These estimatesindicate that
themagmadischarge
ratedecreased
from9 x 10s to 3 x 10s kg/sduringtheeruption.
The grain-sizedistribution at the top of the eruption column is characterizedby
depletionof coarseclasts,suggestinga distinct decelerationin the gasthrust region
down to severaltens of meters per second,particularly during the secondhalf of
the climactic phase. The total amount of layers C1 and C: is estimated to be
3 x 1012kg, and the veryfine particles,whichdid not depositin the accessible
on-land area, may occupyup to 60% of the total ejecta. The effectiveduration of
the eruptionestimatedby the presentmethods(a few hoursor less)is substantially
shorter than a previous estimate from the real-time observation based on infrasonic
data (•-10 hours). This discrepancymay be attributed to the overestimationof the
magma dischargerate due to the entrainment of the ambient air at the cloud top
and/or to the underestimation
of the total amountof the ejectadue to the effect
of the contemporaneous
Plinian activity and generationof pyroclasticflows. It is
also suggestedthat the intensity of eruption was fluctuating with time so that the
instantaneousobservationssuch as cloud height in satellite images do not always
show a quantitative agreementwith the time-averagedfeatures predicted by the
present methods.
1.
Introduction
of tephra is also affected by the presenceof wind. We
have introduced
This paperand the companionpaper (paper 1) [Koyaguchiand Ohno,this issue]are concernedwith inversion methods to reconstruct eruption column dynamics from granulometric data of Plinian deposits. The
methods are based on a dispersal model which assumes
some idealized conditionsof eruption; for example, the
umbrella cloud is assumedto expand steadily due to a
continuousPlinian eruption. In reality, some Plinian
eruptionsmay be a seriesof pulsating explosionsrather
than continuouseruptions,and they are sometimesaccompaniedby generationof pyroclasticflows. Dispersal
1Now at Department of Geosystem Sciences,Nihon University, Tokyo, Japan.
some statistical
treatments
to evalu-
ate various kinds of noise in data and assessed some of
the major assumptionsfrom the theoretical viewpoint
in paper 1. However, it is not clear how these effects
modify actual resultsof the presentmethods.
In paper 2, we apply the methods to the tephra fall
deposit of the Pinatubo 1991 eruption. Because the
sequenceof eruption and the behavior of the eruption
cloud were witnessedby real-time observations,such
as monitoring of seismic and acoustic waves and remote sensingof eruption cloudsfrom satellites, we can
test the presentmethodsby comparingthe resultswith
these observations.This study is an extensionof pre-
viouswork [Koyaguchi,
1994,1996].The presentstudy
Paper number 2000JB900427.
is basedon a more comprehensiveset of granulometric
data than the previouswork; it includesmodal compositional analysesfrom different fall units, which provide
new informationsuchas the waxing and waningof the
0148-0227
/ 01/ 2000JB900427509.00
eruptive mass flux and an estimate of the total amount
Copyright 2001 by the American GeophysicalUnion.
6513
6514
KOYAGUCHI AND OHNO: RECONSTRUCTION OF ERUPTION COLUMNS, 2
of ejecta.Theseimprovements,
aswellasmoresophis- 2. Tephra Fall Deposits of the Pinatubo
ticated inversionmethodsdevelopedin paper 1, enable 1991 Eruption
us to quantitativelycomparethe resultswith real-time
2.1.
General
Features
geophysical
observations
fromdifferentpointsof view.
In section2 the generalfeaturesof the Pinatubo1991
Repetitive explosiveeruptionsoccurredat Mount
eruptionandthe tephrafall deposits
are described.
In Pinatubo,Philippines,beginingon June 9 and culmiorderto clarifyhowthe presentmethodsare applicable natedon June 15, 1991 (for detailsof the eruption,see
to past eruptionswe first attempt to reconstruct
the Newhalland Punogbayan
[1996]). The tephrafall decolumndynamicswithout any informationfrom real- positscanbe dividedinto fiveunits(Figure1), desigtime observations in section 3. Then the results will nated as layersA, B, C1, C2, and D in ascending
orbe comparedwith real-timeobservations
in section4. der[Paladio-Melosantos
et al., 1996;Koyaguchi,
1996].
Finally,we discuss
the potentialandthe limitationsof LayersCt, C2, andD correspond
to layersC, D, andE
the methods in section 5.
of Koyaguchiand Tokuno[1993],respectively.
(a)
-__
Layer D?
Fine ash after the major eruption
I
Layer C2
Lapillibearingvolcanic
sand
ß'oo
•. ' 'o
,0-4 0 4 8
/Grainsize(• scale)
\
I
I
Depositsdue to
ø
the climactic
Plinian phase
Layer C 1
Lapillilayer commonly
includingpumicegrains
15 o 00"
of > 1 cm
-
__
o cm
Layer B
Silt size fine ash.
120 ø 00"
--
30"
Layer A
Lapillilayer.
Loc. 1101
(b)
20......... •)'• '
:30"
LayerB
...............
wt
%
•0 4 8
0-4
lO
N
•l-
Grain size (½• scale) 1i 0 kmi
1205
11Ol
15 ø 00"
4 25025
1207
120 ø 00"
1308
30"
Figure 1. Isopach
mapof layersA, B, Ct, andC2 [afterKoyaguchi
andTokuno,
1993;Koyaguchi,
1996](datain mm),andtheirrepresentative
grain-size
distributions.
(a) LayerA and
therepresentative
columnar
section;
(b) layerB; (c) layerC•; and(d) layerC2. Theisopach
map
for layerC2wasdrawnonlyfromthedataonwhichtheeffectof theerosion
is negligible.
The
localities
in whichthe grain-size
distribution
shows
bimodaldistribution
with the modearound
4• areindicated
byopencircles,
andthoseforwhichcompositional
analyses
weremadeareindicatedby opensquares.
Thegrain-size
distributions
from-3.5• to 4• aredetermined
by sieving
analyses,
whilethosefrom4• to 10• arebased
onthescattering
ofa laserbeamthrough
a stream
of particles.
KOYAGUCHI AND OHNO: RECONSTRUCTION
OF ERUPTION
COLUMNS, 2
6515
30
(c)
%
20
lo
3ø"l
Layer
C• o
-4
1003
0
4
8
size (qb scale)
N
10 km
I
1205
80
15 ø 00"
,o
[5
e95
1207
1308
120 ø 00"
30"
(d)
1003
30"
I Layer 0 2
1
20
3
nsize(qbscale)
N
10 km
1205
I
130•
I
1101
64
15 ø 00"
O105
>22
120 ø oo"
30"
Figure 1. (continued)
Layer A is a lapilli or volcanicsand layer enriched
in grayishpumicegrains and lithic fragments. It is
the deposit of the eruption on June 12. Layer B is
a fine ash layer in most locationsaway from the volcano. Eyewitnessaccountssuggestthat there was a
heavyfine-ashfall with rain, evenin the upwindregion,
shortly beforethe lapilli fall of the climactic Plinian
phaseon June 15 [e.g.,Koyaguchiand Tokuno,1993].
'Weconsiderthat most of layer B, especiallythat of the
upwind region, correspondsto this heavy fine-ash fall.
There were pulses of fine-ash fall due to intermittent
minor eruptions on June 13, 14, and in the morning of
ers, and they are the recognizedfall units producedby
the climactic Plinian phaseof the eruption on the afternoon of June 15. Layer D is a fine-ashlayer originating
mainly from fallout of semicontinuous,minor eruptions
occurring in the period of June 16 to early August.
The climactic eruption is thought to have featured
contemporaneousPlinian activity and generationof py-
roclastic flows [e.g., Koyaguchi and Tokuno, 1993;
Hoblitt et al., 1996; Scott et al., 1996]. Judgingfrom
the wide distribution and the depletion of coarsematerial, a part of layer B is consideredto be derived from an
energeticash cloud that was producedfrom pyroclastic
June15 mainlyin the downwind(SW) region[Paladio- flowsshortlybeforethe climacticPlinianeruption[KoyMelosantoset al., 1996], someof which could not be aguchiand Tokuno,1993]. The resultsof field studies
distinguishedfrom the depositsdue to the heavy fineashfall shortly beforethe climactic Plinian phasein this
study. Layers C1 and C2 are lapilli or volcanicsand lay-
in the proximal area suggestthat somepyroclastic flow
depositsare interbeddedin layersC1 and C2 [Scottet
al., 1996].
6516
KOYAGUCHI
ANDOHNO'
RECONSTRUCTION
OFERUPTION
COLUMNS,
2
25
2.2. Thickness
and Grain-SizeDistribution
'
I
'
I
'
I
'
I
'
I
'
I
'
I
'
Layer C1
Figure
1shows
isopach
maps
oflayers
A,B,C•,and
'"':.'•
plagioclase
2O
C2afterKoyaguchi
andTokuno
[1993]
andrepresen-
:[• mafic
mineralsl]
tative
grain-size
distribution
analyses.
Allthedataof
grain-size
analyses
(107
samples
from
-3.5½
to10½)
and
compositional
analyses
(57samples
from
-3.5½
to3½) wt
[-] magnetite
15
L• lithic
%
areavailable
onrequest
fromtheauthors.
Thethickness
datawerecollected
in June1991(-•1 weekafter
I noanalyses
10
theeruption)
andDecember
1991.
Thethickness
ofthe
uppermost
partofthetephra
deposits
(layers
Dand/or
C2)decreased
from
June
toDecember
atsome
localities;however,
there
isnosystematic
difference
inthe
ß
ß
ß
ß
1,1,1,1,1,1,1
-4
thickness
oflayerC•between
thedataofJune
andDe-
-2
4.
0
6
8
10
8
10
Grain size (q5 scale)
cember
[Koyaguchi
andTokuno,
1993].
Wecould
not
recognize
anyapparent
change
inbulk
density
ofthedeposits
inthefield
between
thetwoperiods.
These
facts
suggest
thatthedecrease
inthickness
isbasically
due
25
,,,,,
,,,,,,,,,,,,,,,,,,,,,,,
2O
Layer
•
2
toerosion
andtheeffect
ofcompaction
between
thetwo
15
periods
was
limited.
Forlayer
C2wedrew
anisopach
wt %
maponlyfromthedataonwhich
theeffect
oferosion 10
is negligible.
Theisopach
mapoflayerA shows
a narrow
distri-
bution
withanaxisextending
southwest
fromthevent.
5
Thegrain
size
oflayer
Arapidly
decreases
withdistance
fromtheventalong
theaxis.LayerB andthetephra
fallunitsoftheclimactic
Plinian
phase
(layers
C1and
0
--m'-•-m -4
-2
0
2
' ........
4
6
Grain size (4• scale)
C2)arewidely
distributed
inalldirections
including
the
upwind
side
(NE)ofthevent,
although
they
areslightlyFigure2. Typical
results
ofcompositional
analyses
of
elongated
inthedominant
winddirection.
Layer
B is layerC• andlayerC2(theresults
oflocation
1101at
mostly
composed
ofsilt-size
fineash(-•4½),
butit con- 14.2kmSWfromthevent).SeeFigureI forthesample
tainssmallamounts
oflapilligrains
in thedownwindlocality.
direction
(SW).Layer
C• isa lapillilayercommonly
including
pumice
grains
of>1 cmin diameter.
Layer
C2isa lapilli-bearing
volcanic
sand
layer.Thegrain2.3. Modal Compositionand Bulk Density
of the Deposits
sizeof layers
C1andC2alsodecreases
withdistance
fromsource;
however,
therateofthedecrease
ismuch Theweight
fraction
offreeplagioclase
crystals
ismea-
slower
thanlayerA. LayerC2contains
a smallto con- sured
forallthesieved
samples
oflayers
C1(29samples)
siderable
amount
ofsilt-size
fineashandshows
bimodalandC2(28samples).
Among
them
modal
compositions
sizedistribution
inalmost
allareas
except
tothesouthofallthecomponents
aredetermined
for11and7 samof Pinatubo.
Thepresence
ofthesecond
mode(finer ples
fromlayer
C1andlayer
C2,respectively
(fortheir
than4•b)
inthegrain-size
dataoflayer
C2maysupportlocalities,
seeFigure1). Typical
results
ofthecompotheideathat therewaspyroclastic
flowactivityaccom- sitional
analyses
areshown
in Figure2. Thedeposits
panying
thePlinian
activity
during
deposition
oflayerarecomposed
of 27to 55wt % pumice,
43to 65wt
C2.
%
free
crystals,
and
<9
wt
%
lithic
fragments.
Pumice
Thecalculated
terminal
velocities
ofparticles
in lay-
grains
aredominant
intherange
between
-3.5•b
and
ersC•andC2indicate
thatthese
deposits
arebasically
-l•b.
Predominant
free
crystal
particles
are
plagioclase
composed
ofclass
II fragments.
Ontheother
hand,crystals
ranging
from-l•bto3•b.
Theproportion
offree
thefineashoflayers
B andC2felloutaccompanied
by
crystals
is
higher
in
layer
C•
(64
wt
%)
than
in
layer
C•
muddy
rainfall,andtheyareconsidered
tooriginally
(52
wt
%).
The
qualitative
features
of
modal
composibelong
toclass
III. Judging
fromthefactthata largetion(i.e.,predominant
constituents,
difference
between
pumice
cone
was
probably
notformed
bythiseruption,
layers
C•
and
C2,
etc.)
are
basically
invariable
within
weassume
thattheproportion
of class
I fragments
is
the accessible
area,although
thequantitative
features
negligibly
small
except
forthose
inthepyroclastic
flow
to someextent.
deposits
formed
bythiseruption.
In section
3 wewill vary
Reconstructed
bulkdensities
of thedeposits
(Psed)
reconstruct
thedynamics
oftheeruption
cloudduring
weredetermined
bymeasuring
thevolume
andweight
theclimactic
Plinian
eruption
using
thegranulometric
of
each
sample
before
sieving
analyses
in
the
laboradataof layerC• andlayerC2.
KOYAGUCHI AND OHNO: RECONSTRUCTION
2000
ß LayerC•
o LayerC2
'•E 1500
1000
'5
500
6517
C1 and 1250kg/m3 for layerC2) in determining
mass
of depositsper unit area usingequation (13) of paper
1. Although we carefully reproducedthe appearance
o e•
• @0
.i i i i I i ß ß , i , i , , i , , , . i ß , ! , i • i i •
10
COLUMNS, 2
of the deposits during this measurement, the samples
tend to be slightly more compacted in the laboratory
than the actual depositsin the field. As a result, the
laboratory-measureddensitiesare expected to be systematically greater than the bulk densitiesin the field
o
o
ßi
=
OF ERUPTION
15
20
25
30
35
40
Distance from the vent (km)
Figure 3. Bulk densities measured in the laboratory
of samplesof layer C1 (solidcircle) and layer C2 (open
circle)as a functionof distancefrom the vent.
(errorsin the bulk densitiesare estimatedto be lessthan
a few tens of percent). Becausethis effectbiasesall the
results equally, the relative tendenciesof the above results must be robust. Accordingly,the estimation of the
expansionrate of the cloud will not be affected by this
error. On the other hand, the total mass of the ejecta
based on these laboratory-measured densities may be
overestimated
3.
to some extent.
Reconstruction
of Plinian
Column
tory. The bulk density of layer C2 is systematically
Dynamics on the Basis of Granulometric
greater than that of layer C1, reflecting the different
Analyses for Layer C1 and Layer C2
modal composition, but they are constant within each
layer regardlessof distancefrom the vent (Figure 3).
In paper 1 we have developedtwo inversionmethods:
We usethe average
valuesof Psed
(1000kg/m3 for layer methods 1 and 2. Method 1 provides the expansion
(a) Layer C 1
4
.
,
.
,
.
,
.
,
.
,
.
,
.
,
o NEI
.
ß
4
f............
o •o : •, ßnSEI
:]
2
ßo•. ß
ß swI
0 ß 0 ß
0
......
. , . , . ,
o NEI
nSEI
o NWI
o NWI
2
ß SWI
(y)
0 O0
0ß ßO•o ßß0
roO•o
0
-2
-4
-4
-1 .sq•
-6
0
0
2.5q•
4
8
12
16
16
4
2
1•0
ßo'•O
0
-4
0
•
ß
'
-
•
-
'
-
-
1'2
'
-
16
2
-2
-4
-4
, .•.
,.;•.,
-6
.•
o
ß ' ' • ' ' ' •1' ' ' 1'2' ' '16
,
ß
0 ß O ßß
0
-2
ß
o i•1
ø
ßo
1.0•
ß , .;,.
2
0
-2
-3.0•
0
'
0
--
o
-6
ß
r--
o
-2
0
4
4
2
-6
,
ß
,
ß
,
ß
i
ß
,
ß
,
ß
,
Oooo•o
t o•lt•
ø
ß
0 ß OE•'
o
-6
0
ß
o
o
-4
-2.5 q•
-6
,
i
,
•.5•
,
i
ß
ß
,
ß
ß
,
ß
ß ''•'
ß
r ß,.,oo,•& ß 40
,
oo
ß
ß
' '•''','•''
i
.
ß
0o%
o
,
ß
,
ß
,
ß
o
,
-
,
ß
o
oo
oI -o
-2
ß
-4
ß •l•O
-60t -?-"0
•
' ' 4'
' 8'
0.0•
'1'2' ' '
(distance?
from
the
vent
(x10
sk•26)
(distance?
fromthevent(x10skm2)
4.0•
2.0•
0 ' ' ' •1 ' ' ' • ' ' '1'2' ' '16
(distance)
2fromthevent(x10s km2)
0
ß
0
ß
4
8
12
16
(distance?
fromthevent(x10s km2)
Figure 4a. Relationshipsbetweenlogarithmof massof depositsper unit area for individual
sievingintervals(0.5½interval)and squareof distancefrom the vent for data of layer C1. The
plotsof differentdirections
from the vent are shownby: opencircle,NE of the vent (upwind);
open square,SE of the vent; open diamond,NW of the vent; solid triangle, SW of the vent
(downwind).
6518
KOYAGUCHI
(b)LayerC2
4
.
,
.
,
.
,
.
,
.
,
.
,
ß ,
AND OHNO' RECONSTRUCTION
ß
4 ....
2
0
ßo•
oo-ß
o•o
-2
COLUMNS,
[] SE
O N¾
ß SW
: ß%
.
o g•
[] [] ßA 0
2 Ooo• ß •[] ßß O
o
o•o
o
o NE'I
[]SEI
o NWl
-4
1 .o•
-1.0•
-6
3.0q•
,
-6
0
4
8
12
16
0
4
2
8
-2
•O•)
o•,
o
ß
i
ß
,
ß
,
4
12
ooO•
ßß ß
o
o•
ß
o
-2
-4
AO
2
. , oNE
ß
0
O
. .....
OF ERUPTION
,
i
8
,
i
,
i
i ß swI
,
i
ß
12
i
16
ß
o
o
ß
ß
ß
000
-2
-4
-4
-2.5•
-6
,
,
o
,
,
3.5•
1.5•
i
.....
,
-6
ß
0
4
8
o' '';''
12
'•'
'';•'
'
2
000•00
0
o
0
[][]
-2
ß
ß
•O_o ß
oo • o
-4
4.0•
2.0•
-6
-6
0
4
16
.
,
.
,
.
,
.
,
.
,
ß ,
.
,
.
ßo-•,,
00"'• %
ß o%1,
ß
o
i[ ooo•
O []
-6
t -1.5
q•
-o''';''''8''
42
o
2.5•
0.5•
'
0
(distance)
2from
the
vent
(x10
8k•
o
o
ø1: •'Oor :
-
:o,•
o' ''•,''
'•'
'';•''
distance)
2fromthevent(xl08 km2)
4
8
12
16
(distance)
2fromthevent(x108km2)
(distance)
2fromthevent(x108km2)
Figure 4b. Sameas Figure 4a exceptfor layer C2.
rateoftheumbrella
cloud(lk) andthemassofdeposit able for grain sizesbetween -3½ and 1½, whereasit
per unit area in the ith range of grain size at the vent
ß
is lessobviousfor coarseror finer grain sizes. The rate
(Si(O)). Method 2 providesV for individual localities. of decreasein the mass with distance is systematically
It has been suggestedthat method I is more useful for higherfor coarsegrain sizesthan fine grain sizesfor the
evaluating the uncertaintiesof the granulometricdata. samplesfrom the southwestregionof the vent (i.e., the
Because the evaluation of the error is one of the main isdownwindregion). Thesefeaturesare qualitativelyconsuesof this study, we first carry out method 1, and then sistentwith the tephra dispersalmodel [Bursiket al.,
method 2 is used in interpreting the results of method 1992;Koyaguchi,1994].
1. All the notations used below follow those of paper 1.
Fromthe relationship
between
In Si(r) andr 2 in Fig-
ure4,wecandetermine
1/1•andS•(0)foreachrange
of
3.1.
Determination
by Method
of the Model
Parameters
1
Method I is based on the relationship between the
grain sizeby applying a least squaresmethod to equation (14) of paper 1. As wasmentionedin paper 1, two
proceduresare necessaryto carry out method 1. First,
because
theestimates
of 1/1•ifromdifferent
ranges
of
logarithmof massof depositsper unit area and the grain size do not always give a consistentvalue, the
squareof distancefrom the vent (Figure4). The mass weighted
average
(1/l•win equation
(17) of paper1)
of deposits
per unit areais obtainedfromequation(13) must be calculatedfrom 1/1// (seeFigure 4 in paper
ß
of paper 1 for individualsievingintervals(0.5½interval) 1). Second,an appropriatereleasealtitude must be
usingthicknessdata (T(r)) and the averagevaluesof determined by the intersection of the relationship berelease
altitudesandlkwandthe possibulk densityof the deposits(Psed(r))-For layer C2 we tweenassumed
adopted interpolated thickness from the isopach map ble rangeof the relationshipbetweenneutral buoyancy
instead of the actual thickness data for some localities
level (NBL) and volumetricflowrate at NBL (seeFigin order to avoid the effect of erosion.
ure5 in paper1). In practice,
wedetermine
1/1•wand
The logarithmof the massper unit area (ln Si(r)) lin- Si(O) usingterminalfall velocities(vi) for releasealtiearly decreaseswith the increasingsquare of distance tudes of 20, 25, and 30 km as auxiliary variables. Most
(r2). The linear relationshipis particularlyremark- of the results shown in the diagrams are based on the
KOYAGUCHI AND OHNO' RECONSTRUCTION OF ERUPTION COLUMNS, 2
(a)1.2
ß
I
'
I
'
I
'
I
(b)1.2
'
'I'I'I
LayerC• (SW)
o
._•
LayerC• (NE)
1
standard
0.8
deviation
ß 0.8
o
standard deviation
ß
u• 0.6
& 0.6
'u
0.4
• 0.4
'd
0.2
'•.
0
-4
-3
-2
-1
0
1
-
v
2
•,• v
3
0.2
coefficien•
i i i , I . , , , I , , , , I , u
O
4
ß
-4
-3
-2
Grain size (½ scale)
1.2
'
I
'
I
'
I
'
I
'
I
'
I
'
I
1.2
'
standard
,, I , . . ,'•IF'"I,,•_,
-1
0
1
_ _
A,•, •,,•, , ,i•,
2
,• , ,
3
4
Grain size (½ scale)
,,•1,•,,i,,,,
LayerC2(SW)
•o
6519
i,,,,1•,,,
i,,,,i,,,,
i,,,,
LayerC2 (NE)
deviation
standard
0.8
deviation
ß 0.8
o
& 0.6
.
._
nt•l•.•
'u 0.4
'
ß
weight coefficie
oß' .' '
'd 0.2
-4
-3
-2
-1
• 0.4
w
ß ocoeficient ••,•
'•.
0.2
....
0
1
2
3
4
Grain size (½ scale)
-4
I
-3
....
I,
-2
,,,
I,,
-1
--
I
....
0
T ,•"",•,--..•k
1
,
2
,,-.
, •,
3
....
4
Grain size (½ scale)
Figure 5. The standarddeviationof the relationship
betweenIn Si(r) and r 2 andthe weight
coefficient
as a functionof grainsize(•bscale)for layersC1 and C2 for (a) data from SW of the
vent and (b) data from NE of the vent. Seepaper I for the definitionof the weightcoefficient.
terminal fall velocitiesat 25 km, but the results for 20
Figure 5 shows the standard deviation in the relaand 30 km are alsolisted for comparisonin sometables. tionship between the logarithm of the mass per unit
Subsequently,
wedeterminepreferablerangesof release area and the square of distance from the vent as a func-
altitude and corresponding
preferablerangesof other tion of grain size (•b scale). The valuesof the standard deviation are large for fine and coarsegrain sizes.
The granulometricdata in Figure 4 contain at least This is consistent with the impression that data are
three kinds of errors;those are (1) errorsdue to re- scatteredfor fine and coarsegrain sizesin Figure 4.
gionaleasterlywindin the stratosphere,
(2) errorsdue The secondand third sourcesof errors would explain
to localwind at loweraltitudes,and (3) analyticaler- the large standard deviation of fine and coarsegrain
rors during sievinganalyses.The shapeof the isopach sizes, respectively. The wind at lower altitudes such as
maps (Figure 1) suggests
that there is considerable
ef- that due to typhoonYunya [Oswaltet al., 1996]is exfect of the easterlyregionalwind in the stratosphere. pectedto locally modify sedimentationrate particularly
The relationshipbetweenthe mass per unit area and for fine particles with terminal fall velocities smaller
the distancefrom the vent also dependson direction than the local wind velocities. Sieved samplesin the
from the vent;the massper unit areais systematically range coarserthan -3.0•b contain only a small number
greaterin the downwind(SW) regionthan the upwind of grains(<10 grainsat somelocalities).The resultsfor
(NE) andotherdirections
(Figure4). The systematicsuchrangeschangeup to 10%, dependingon whether
parameters.
changein the rate of decreasein the masswith distance
one grain passesthe mesh or not.
depending
on grainsizeis not evidentfor the samples Figure 5 alsoshowsthe weight coefficientdefinedby
of the upwindregion.The effectsof the regionalwind equation(18) of paper I asa functionof grain size. The
will be examinedby performingthe inversionmethods weight coefficientincreasesas the standard deviation of
for the upwindanddownwind
regionsseparately
in the data decreases,and as the curvature of the error as a
followinganalyses.More quantitativeevaluationfor the functionof modelparameters(Ei(m)) at the minimum
effectof the regionalwind is givenin AppendixB.
becomes
narrower(seeequation(18) of paper 1). The
6520
KOYAGUCHI
AND OHNO' RECONSTRUCTION
(a) 2
OF ERUPTION
(b)
COLUMNS, 2
LayerC• (NE)
20km
4
1.5
•'
1
-•0.5
ß
-4
I
.
-3
I
.
-2
I
-1
ß
I
.
0
I
.
I
1
2
.
3
.
0
I
I
.
I
-3
-4
4
3 o%._.,•
,•
.
-2
I
,
-1
I
.
I
0
.
I
1
,
2
I
.
3
Grain size (½ scale)
Grain size (4• scale)
2
LayerC2 (NE)
4
ß
20km
30
ß
-4
-3
-2
-1
0
1
2
3
I
-3
4
.
I
-2
Grain size (4• scale)
ß
I
-1
,
I
0
ß
I
ß
1
I
2
.
I
3
Grain size (½ scale)
Figure6. Theinverse
oftheexpansion
rate(1/lfi)asa function
ofgrainsize(½scale)
estimated
by method1 for layersC1 and C2 for (a) data fi'omSW of the vent and (b) data fromNE of the
vent. The estimatesfor individualrangesof grain sizeare normalizedby the weightedaverage
(1/½w).
curvatureof Ei(m) at the minimum dependson termi- 7). On the other hand, the eruption column dynamnal velocity;Ei(m) has a broaderminimumfor smaller ics model [Woods,1988] predictsthe relationshipbeterminal velocities. The weight coefficientis small for tweenNBL and the volumetricflow rate at NBL (VNe).
.
particles finer than 0½ for both layers C• and C2 because Becausethe release altitude is roughly equal to NBL,
of the large standard deviations and broad minima of the actual expansion rate can be obtained at the inEi(m). From these featuresof weight coefficientit is tersection of the two relationships between expansion
inferred that the estimated model parameter is largely rate and altitude. The effectsof the regional wind are
determined by the data of coarseparticles and that the crudely evaluated using the approximation in section
effect of local wind
does not much affect the estimation
of the expansion rate.
6.2 of paper 1 (seeAppendixB for procedures).When
the effect of the regional wind is taken into account,
Figure 6 showsthe inverseof the estimated expansion
theestimate
of lkwsystematically
decreases
fora given
rate for individualrangeof grain size (½ scale)normal- releasealtitude (Table B1 in AppendixB). The prefer-
of lkwaredetermined
bythepossible
range
izedbytheweighted
average
(Vw/l/i).Forthedataof ableranges
the downwind
(SW) regionthe estimates
of 1/lfi for
different ranges of grain size are consistent as far as
Expansion
Ratel/w Determined
the ranges whose weight coefficientshave high values Table 1. Volumetric
are concerned. This result suggeststhat the basic as- by the GranulometricInversionMethod I a
sumptionsof the dispersalmodel (seepaper 1) are appropriate for these ranges of grain size. We adopt the
weighted averageof these data as the best estimates of
the expansionrate for a given releasealtitude (Table
1).
The results in Table 1 give a relationship between
assumedrelease altitudes and Vw estimates (Figure
AssumedAltitude, km
Layer C1
Layer C2
20
25
30
6.8 X 1010
9.2 X 101ø
12 X 101ø
3.2 X 101ø
4.3 X 101ø
5.6 X 101ø
ß
alnm3/s.
KOYAGUCHI AND OHNO: RECONSTRUCTION
=
o
E'•'
OF ERUPTION COLUMNS, 2
6521
Figures 8a and 8b show the variation of estimated
15
1) bymethod2 ona mapof theareaaroundPinatubo.
Range predictedby the eruption
column dynamics model
(Woods, 1955)
Lay•i•3C
1(•=0x10
-6) There are someregionaltendenciesin the estimated val-
uesof 17bymethod2. Forthedatafromthedownwind
(SW)regiontheestimates
of1)bymethod2 areconsis-
10
LayerC1 ( • =5 x 10-6)
tent with those of method
1. For localities
in the west-
•ayerC2(a=0x10-6) ern region,1) by method2 tendsto givea relatively
o
ß X
-,--'
5
large value. The expansionrate has negative valuesfor
layer C1 at somelocalitiesin the upwind (NE) region,
which implies that the depositsbecomecoarser-grained
mmmm
ß m• mß
LayerCz( • :5 x 10-6)
mmmml
mm
O
.m
•
x
as the distance from the vent increasesin the upwind
0
10
15
20
25
30
direction.
35
The meaning of the results becomesclearer by taking
Altitude (km)
the value
Figure 7. Diagram showingpossiblerangesof the altitude of the umbrella cloud and the expansionrate. The
range is determined by the intersectionof the relation-
1 -- St,
(1)
ship basedon the eruptioncolumndynamics[Woods, where1)1and1)2arethe expansion
ratesestimated
by
1988]andtheestimated
expansion
rate(l/w)asa func- methodsI and 2, respectively(Figures8c and 8d). The
tion of assumedreleasealtitudes (shadedzone). The
value of 5t has a meaning of the differencein estimated
possible
ranges
of therelationship
between
l/wandre- travel time betweenmethod I (tl) and method 2 (t2)
lease altitudes are based on the results before and after
as
the correctionof the effect of regionalwind (Tables 1
and B1, respectively).
t2 -- tl
tl
(2)
(seeequation
(3)of paper1). Considering
that I7•is a
of NBL versus
I)NBrelationship
andtherangebetween kind of spatial average,the magnitude of 6t is regarded
as a measure of the deviation from the average travel
the resultsof Table I and Table B1 (shadedareas in
Figure7). They are 5-9 x101øma/s for layerC1 and time of the umbrella cloud. In (2) both the localities
whichhavenegative
1)2andthe localities
where1)2>
2.0-3.5 x 101øma/sforlayerC2. Thepreferable
ranges
1)•shownegative
anomaly
of 6t. Therearezonesof a
of releasealtitude are 22-25 km for layer C1 and 20-22
km for layer C2. These results will be compared with
real-time
observations
negative anomaly of 6t in the western region for both
layers C• and C2 and that of a strong negative anomaly
in section 4.
Fortheupwind(NE) region
thevalues
of (1/•i) es- in the upwind (NE) regionfor layer C•. It is inferred
that the averagetravel time of the cloud was relatively
timated from different ranges of grain size are diverse
even for the rangeswhoseweight coefficientshave high
short for these localities.
The strong negative anomaly of 5t for layer C• in
values(Figures5 and 6). This featuresuggests
that the
the upwind region indicates that the intensity of eruppresentinversionmethod (method 1) is inappropriate
tion was fluctuating and only intensivepulseswith high
for the samples of the upwind region. Possiblemechexpansionrate (short travel time) selectivelyreached
anisms that lead to the relationship between the mass
the
upwindregion. The thickness(massper unit area)
per unit area and the distance for the upwind samples
in
the
upwind region systematicallydecreaseswith the
will be considered below on the basis of method 2.
distancefrom the vent (Figure 4). This is interpreted
3.2. Supplementary
by Method 2
to reflect the fact that the number of the pulses which
could reach the upwind localities decreaseswith the increasingdistance from the vent.
Interpretation
The most unrealistic assumptionthat leads to diverse
1)/by methodI forthe upwindregionis that effective
duration of deposition(ra) is constantthroughoutthe
investigatedarea. If the intensity of eruption was fluctuating, the umbrella cloudsof weak pulseswere largely
conveyedby the regional easterly wind and they could
not reach the upwind region. As a result, the effective duration of depositionmay have been substantially
shorter in the upwind region. Becausemethod 2 does
not assumethe constanteffectiveduration (see equations (9) and (10) of paper 1), we can apply it to the
upwind samples to interpret the relationship between
the mass per unit area and the distance.
3.3. Size Distribution
at the Top
of the Eruption Column
Grain-size distribution of class II fragments at the
top of the eruption column (i.e., at the center of the
umbrella cloud) is estimatedfrom $i(O)/vi (compare
equation (7) of paper 1). The valuesof $i(0) are redetermined by applying a least squaresmethod to the
samplesfrom the downwind(SW) regionwith a fixed
auxiliaryvariableof l/wfor all the ranges
of grainsize
(Table 2). We can also calculategrain-sizedistribution of class II fragments at the top of the eruption
6522
KOYAGUCHI AND OHNO: RECONSTRUCTION
OF ERUPTION COLUMNS, 2
columnfrom S• (0), whichis determinedby the simple 3.4. Total Amount of the Ejecta
leastsquares
method
withoutfixed1• (Table2). The
We estimate the total amount of class II and class III
differencebetween the results by the two least squares
methods is not significant.
fragments(SII+iII) on the basisof the dispersalmodel
The results show that classII fragments in layer C2 and the idea of Walker's[1980]crystal concentration
are systematicallydepletedin coarsefragments(<0•b)
comparedwith layer C1 (Figure 9). It is inferredthat
there were somedifferencesin sortingprocesses
in rising
eruption columns or possibly differencesin fragmentation processesduring explosionsbetween layer C1 and
layer C2.
method (see paper I for detailed method) as an approximate total amount of ejecta. Becauseplagioclase
is the predominantfree crystal in the deposits(Figure
2), the methodis appliedto the data of the massof free
plagioclasecrystals per unit area.
Figure 10 showsthe mass of classII plagioclaseper
Layer
C1 0
Q(Method
2)( X1 m/s) _=-2
,
•e 10.s
'fO 20 40 60 80
. ß.7.0
•ßß16.2
21.4
15 ø 00"
r- 0904 / so(sw) I.
A I,,,I,,,IH-'I';'O'
• Terminal
fall
velocity
¸)
s
15;1
- ;;, ,-4.1
-2.7_4].
5
3
0'4'9•-7'3
19.7 /"1' .-6.1
W
,3.2
_ .8.1o624'3'•13•"6••1
'-
-
oß
,29,4,
(,s,0,(S,
,vv),,,,
',6.7•';
•'•9
12.1
•.5 '
•0km
•.1 8.4 '
-
I
30"
120 ø 00"
(b)
:80"
ß
10
3
e- -2
V(Method2)(X10
m/s)-.ztI0904/s0(s,,,,,,,,,,,,,,i,,
/0
20 40 60 80 100
6;1
ß3.6
\
._.
/Terminalfallvelocity
(m/s)
-;
/.18.4
82
/
15 ø 00"
6.1.7',
8_.4.1
•__
71.7,,'
- i '5'7 3.21.2..3.••
/.
5.8.. 5.6 '9.7
•3.9
7.0
11..9
7•
•
10.2
L
120 ø 00"
I
/,•
-I
Itt•,
•_
J
,
' T-'•
-I
_l U
--
32•1204/S0(S
W) 4//1
m
47 i I,,,I,,,•,,,i,,,l,,,m
'
,
•Okm,
30"
Figure8. Mapsshowing
theexpansion
rateestimated
bymethod
2 (1•)andthedifference
in
estimatedtraveltime betweenmethod2 and methodI (St;seetext for definition).Star indicates
thelocality
ofthevent,anddotsindicate
sampling
localities.
(a)l/for layerC•;(b)1•forlayer
C2; (c) 5t for layerC1; (d) 5t for layerC2. Representative
resultsof the relationship
between
InR(r, v) andv areshown
in Figures
8aand8b. Forthedefinition
ofinR(r,v) seeequation
(10)
of paper 1.
KOYAGUCHI AND OHNO' RECONSTRUCTION OF ERUPTION COLUMNS, 2
6523
(c}
I
I
i
Layer C1
N
½t
-1.0
)"04-0'14 -3.3'
-4.0•.0
10 km
. ".0.33\_•
. -0.53'•/-2.51
ß
-
1 5 o 00"
I
-4.40 -3•04
.1.91
.2_._0.32
.
0.31
.
0.24
63 /
0.19
_•,,•.._34-0.03'
0 30 -"040 '
g
ß
I
1zo ø oo"
30"
(d
I
i
i
Layer C2
dt
N
.0.29
.0.21
-0.28
•
;0.22
-0.29-.0,4_4:0.07
-./•6-2:10'
/.
ß e0
15
ø00"I-'0.23
n••O•-.6:•a
';.••
48
,
0.•0 -0.38•
•;06/ o.26
;0.09
e0.37
120 o 00"
30"
Figure 8. (continued)
unit area against the square of distance from the vent. from Si(O) and Xi(O) usingequation(22) of paper 1
These data show scatter due to large errors because (Table 3). The rangesof thesequantitiesfor the preferof complicated procedures required to determine the able release altitudes are determined in a similar way
massof plagioclasecrystals (sievingand modal analyses). The massof classII plagioclaseat r - 0, Xi(0),
is obtained from these data usingthe same relationship
as equation(14) of paper 1. In order to avoid the effect of the large errors in the plagioclasedata we used
the valuesof Vw basedon the bulk deposits(Table 1)
and the terminal velocitiesof plagioclase(the relation-
to thoseof l/w (compare
Figure7). The effectof re-
The total amount of classII fragments and that of
classII plagioclasecrystalsin the depositsare obtained
timated from that in juvenile fragments.The juvenile
fragmentsof the Pinatubo 1991 eruption are divided
ß
gional wind is taken into accountusing the results of
Table B2 as well as Table 3. The preferableestimatesof
the total amountof classII fragments(Sii) are 5.3-8.3
x10TMkg for layerCz and 5.3-8.2 x10TMkg for layer
C2, and thoseof the total amount of classII plagioclase
are 2.8-4.5 x10TMkg for layerCz and 2.9-4.6 x10TM
shipfor Pclast
-- 2700kg/m3 in Figure3 of paper1) as kg for layer C2.
auxiliary variables in the least squares calculations.
Modal abundanceof plagioclase
in the magmais es-
6524
KOYAGUCHI AND OHNO: RECONSTRUCTION OF ERUPTION COLUMNS, 2
Table 2. Massper Unit Area at the Vent (Si(O)) Determinedby Method
Layer C1
q5
20 km
25 km
Layer C2
30 km
SLSMb
20 km
25 km
30 km
SLSMb
-3.5
3.5
4.2
5.2
3.2
0.0
0.0
0.0
0.0
-3
3.8
4.8
6.6
3.1
0.0
0.0
0.0
0.0
-2.5
-2
-1.5
-1
-0.5
0
0.5
4.6
6.8
5.8
7.4
7.0
7.9
7.6
7.8
2.7
3.8
4.0
4.7
5.4
5.2
8.4
8.5
8.6
8.6
8.9
8.6
8.8
8.6
5.5
5.4
5.9
5.6
6.3
5.7
I
13.9
13.2
17.5
14.9
13.9
13.1
17.1
14.5
13.8
12.9
16.7
14.1
13.6
12.9
16.8
14.1
10.6
11.7
19.4
21.3
10.7
11.5
18.7
20.3
10.7
11.2
17.8
19.2
0.5
2.9
4.6
5.7
10.9
12.9
20.2
1.5
12.5
12.2
11.9
11.6
25.2
23.9
22.6
23.0
2
2.5
6.2
2.0
6.0
1.9
5.9
1.9
6.6
2.9
19.1
11.3
18.2
10.8
17.5
10.6
19.9
13.6
3
3.5
0.4
0.1
0.4
0.1
0.4
0.1
0.7
0.1
>4
0.1
0.1
0.1
0.1
4.3
0.7
0.2
4.3
0.7
0.2
4.2
0.7
0.2
6.9
1.3
0.2
21.1
aln kg/m2.
bSimple
leastsquares
methodwithoutfixed1• (i.e.,$?(0)) usingthesamples
collected
in thedownwind
(SW)region.
into three types: porphyriticwhite pumice(80-90%)
and crystal-poorgrayish pumice (10-20%) and very
minor andesiticscoria[e.g.,Pallister et al., 1992,1996;
David et al., 1996]. Modal analyseson thin sections
%. The total crystal abundance(includingmicrophenocrysts)of the white pumicegiven in Table 4 (-•70
wt %) is apparentlyhigherthan previousresults[e.g.,
Bernardet al., 1996;LuhrandMelson,1996;Pallister
were carried out for 13 samples of the white pumice
et al., 1996],althoughthe abundanceof plagioclasein
and 2 samplesof the grayishpumicein this study (Table 4). Crystals >0.1 mm in diameter are counted
as phenocrysts(or microphenocrysts)
in these analyses. The white pumice contains44 wt % plagioclase
phenocrystsand the grayishpumicecontains20 wt %
plagioclasephenocrystsand microphenocrysts.Assuming that the ratio of the white pumice and the grayish pumiceis 85:15,the proportionof plagioclase
phe-
Table 4 is consistentwith the result by Luhr and Mel-
nocrysts in magma is estimated to have been •-40 wt
0.5
o
0.4
•
0.3
...,...,...,
..__.LayerC 1
• LayerC2
I
//
///
-
>, 0.2
ß
/
_a 0.1
I"' •'
0
-4
I
-2
multipliedby the modal weightpercentin Table 4. The
calculatedbulk chemicalcompositionon the basisof the
presentresult agreeswell with the publishedbulk chemical composition.
If we assumethat all the plagioclasephenocrystswere
depositedas classII fragments, we can estimate the to-
tal amountsof layerC1 and layerC2 usingequation(25)
of paper I (Table 5). The rangesof the total amount
by this method, in which the preferable release altitudes and the effect of regional wind are taken into account, are determined from the results in Tables 5 and
B3 (compare
Figure7). Theyare0.7-1.1 X1012kg for
layer C1 and 0.7-1.1 X1012kg for layer C2. This result implies that the proportion of class III fragments
is 26-27 wt % for layer C1 and 28-29 wt % for layer
C2. These estimatesare in agreementwith the previous
independent estimates, which are based on the empirical thickness-distancerelationship for on land deposits;
/
o
son [1996]. In order to confirmthe presentresult we
calculated the bulk chemical composition from chemical compositionof each mineral and glasscomposition
0
.
.
.
I
.
,
2
,
I
ß
ß
.
4
6
Grain size (• scale)
Figure 9. Size distribution of class II fragments at
the top of the eruption column for layers C1 and C2.
The estimated model parameters and the terminal fall
theyrangefrom1.3x 1012to 1.9x 1012kg forthe sumof
layersC1 and C2 [PinatuboVolcanoObservatoryTeam,
1991; Scott et al., 1991, 1996; Paladio-Melosantos et al.,
1996;Koyaguchi,
1996].However,for the following
reasons,we considerthat a part of the plagioclasebelongs
that this size distribution doesnot include fine particles
to classI or III due to sortingand/or fragmentationof
crystalsand that the abovevaluesmay underestimate
of classIII, which occupy•-50% of the total ejecta.
the total amounts of the ejecta.
velocities
at 25 km are Used in the calculation.
Note
KOYAGUCHI AND OHNO: RECONSTRUCTION OF ERUPTION COLUMNS, 2
(a) Layer C 1
6525
(b)LayerC2
4
4
2
ß,.,.,.,.,.,.,.]
o
0
-2 •O•oo•
t ß ...
ß
-8
0
i
.
i
4
.
,
o
o NEI:1
8
i
.
,
.
12
16
0
! :o.,,....
4
ß
i
,
8
i
ß
.
!
.
12
0
0
[]
ß
(/)-2
[] SE I-I
o NWI- I
,
ß
o
-4
-6 -1.5•)
2
-4
InSEl
-6
t
ß
-80
16
4
16
,
.
,
0
.
4
,
.
,
.
,
.
8
12
16
4
2
2
0
0
o
•
-2
AA
%
ß
o
(/)-2
-4
-4
-6
-6
0
1.5•
-80
o'''•'''•''';2'''
16
4
4
.
,
.
,.,
,
16
.
,
.
,
.
,
.
,
0
.
[]
-1 .o•)
-8
'''•'''•''';2'''
16
4
2
2
0
0
o
-2
C:-2
-4
-4
-6
o
0
o
(/)-2
-6 2.0•
-8
-80
4
8
12
-8
16
0
4
4
0'-%
-6
...............
0
16
o 0%
-4
-0.5 •
'' '•i''
'•''
'1'2'''16
4
2
2
0
0
"'
o
(/)-2
-2
-4
-4
-6
-6
'80
0:ø.*, ........
4
8
12
,'2'
16
-80
4
•.'o
o
2
0
4[3
o
c:-2
o
o
ß
(p A&
o
-4
AA
ß
o
o
[]
(/) -2
ß
c
0.5•
-8
-8 /
0
4
8
12
16
0
(distance)
2fromthevent(x108km2) (distance)
2fromthevent(x108km2)
-4
-6
0.5•
-80' ' ''i'
AA
ß
ß
o
c -2
4
-6
_
2
0
' '•'
....16
' '1'2
-6 3.0•
80
4
..........
8
12
16
(distance)
2fromthevent(x 10skm2) (distance)
2fromthevent(x 10skm2)
Figure 10. Relationshipsbetweenlogarithm of massof plagioclasefree crystalsper unit area
for individualsievingintervals(0.5½interval) and squareof distancefrom the vent for (a) data
of layer C1 and (b) data of layer C2. The symbolsare sameas Figure 4.
The first reasonis that the sizedistribution of plagioclase at the top of eruption column, which is obtained
crystalscomparedwith that in the magmaand its range
is similarto that of the bulk depositsfor both layersC1
from Xi(0), deviatesfrom the originalsizedistribution and C2 (Figure9 and Figure 11). It is suggested
that
in the magma, which is obtained by carefully crushing plagioclasecrystalsand pumicegrainsare influencedby
juvenile clasts or by calculating from two-dimensional a common sorting processduring transportation.
size distribution in thin sections. It is depleted in coarse
The second reason is that some observations
indicate
that considerableparts of plagioclasephenocrystswere
fragmented
and becameclassIII fragments. First, the
Table 3. Total Amount of Class II Fragmentsand
proportion of fragmentedcrystals is higher in the free
ClassII PlagioclaseDeterminedby Method I a
crystalsof the tephra fall deposits(•90%) than the
Layer C t
Layer C2
phenocrystsin thin sections(•,-50%). Second,the obser20 km
25 km
30 km
20 km
25 km
30 km
vationsusingthe scanningelectronmicroscope(SEM)
indicatethat the fine-ashdepositscontainangularfragClass II Fragments
ments, which are consideredto be fragmented crystals
7.5
8.3
9.4
7.7
8.8
10.0
as well as fragments with bubble wall surface. The fol(0.18)
(0.18) (0.19)
(0.069) (0.074) (0.079)
lowingtwo observationswouldalsosuggestthat part of
plagioclasephenocrystsmust have beenfragmentedto
Class H PlagioclaseFree Crystals
becomeclassIII fragments.
4.1
4.5
5.1
4.3
5.0
5.8
In the Pinatubo case,fine ash fell out as aggregates
aln unitsof x10TMkg. Numbersin parentheses
indicate accompaniedby "muddy rain fall" or as accretionary
the amountof pumicelargerthan classII plagioclase
(Sp). lapilli to form layer B or to lead to the bimodal size dis-
6526
KOYAGUCHI AND OHNO: RECONSTRUCTION
OF ERUPTION
COLUMNS, 2
Table 4. Modal Composition
in JuvenileFragmentsof Table 5. Total Amount of Ejecta Determined by the
Modified Crystal Concentration Methoda
Pinatubo 1991 Eruption a
WhitePumice
b GrayPumice
c Bulkd
LayerCt
20 km
Quartz
2.6
0.9
2.3
Plagioclase
43.9
20.2
40.3
Biotite
Hornblende
Fe-Ti oxide
Other minerals
Matrix
Total
1.0
18.1
2.9
0.8
30.7
100.0
0.3
5.5
1.6
1.0
70.6
100.0
0.9
16.2
2.7
0.8
36.7
100.0
aln wt %.
bAverageof 13 samples.
cAverageof 2 samples.
dAverageassumingthat white pumice: gray pumice -85:15.
25 km
Layer C2
30 km
20 km
25 km
30 km
All the PlagioclasePhenocrystsBelong to ClassH
10
11
13
11
12
15
(27)
(27)
(26)
(29)
(29)
(30)
Proportionof Plagioclasein ClassIII Fragmentsof 27 wt
16
18
20
17
20
24
(53)
(53)
(52)
(56)
(56)
(56)
Proportionof Plagioclasein ClassIII Fragmentsof 25 wt
15
16
18
16
18
22
(50)
(49)
(49)
(52)
(52)
(53)
tribution in layer C2. The proportionof plagioclase
in Proportionof Plagioclasein ClassIII Fragmentsof 29 wt
fine ashcanbe crudelydeterminedby X-ray diffraction
18
19
21
19
22
26
(XRD) (for detailedmethod,seeKlugandAlexander (57)
(57)
(56)
(60)
(60)
(61)
[1974]). Preliminaryresultsindicatethat plagioclase
fragments
occupy27 q-2 wt % of the fineashof layer
aln unitsof x10TMkg. Numbersin parentheses
indicate
C2. Theyalsooccupy35q-2wt % of layerB and•32q-2 the fractionof classIII fragments(wt %).
wt % of fineparticlessmallerthan 4•bin this layer. The
errorsof the aboveanalysesare basedon the standard
deviationof repeatedmeasurements.
Judgingfrom the most of plagioclasein the fine ash is consideredto be
fact that the groundmass
of the whitepumiceis glassy, derived from fragmentedphenocrysts.
Figure 11 showsthat the grain-sizedistributionob--e -in magma (calculatedtrom 2D)
.-.o---inmagma (carefullycrushing)
•
25
-' abovethevent(LayerC•)
abovethevent(LayerC2)
6
amount of classII plagioclasedoes not representthe
total amount of plagioclasein the magma,but it is affectedby fragmentationand sortingprocesses.
The total amount of ejecta can be estimated from
a weak shock.
0
0
2
Grain size (qbscale)
4
the effect of mechanical
.
• d""
-2
in thin sections.
shockduring crushingthe matrix glass;someof the juvenile clastswere dipped into HNO3 solutionfor a few
days before crushing. No systematicdifferencecould
be recognizedbetweenthe resultswith and without the
chemicaltreatments. The resultsof crushedjuvenile
clastsmay supportthat plagioclasephenocrysts
in the
magma are fragile and becomefiner grains with only
5
-4
size distribution
ments in order to minimize
20
10
from two-dimensional
When we determined the crystal grain size by crushing
juvenile clasts, we attempted several chemicaltreat-
. . . , . . . , . . . , ß . ß , . ß ß
wt%
15
tained by carefully crushingjuvenile clastsis depleted
in coarsecrystals compared with that by calculating
These observations indicate
that
the
the supplementary
methodusingequation(26) of pa-
Figure 11. Size distribution of plagioclasefree crys- per 1, if we can somehowdeterminethe proportionof
in classIII fragments.In the presentcase,
tals in class II at the top of the eruption column for plagioclase
layersC1 and C2 (solidcurve) and sizedistributionof it would be reasonableto assumethat the aboveproplagioclasephenocrystsin the juvenile materials. The portionof plagioclase
in the fine ashof layerC2 (27 q-2
size distribution of plagioclasein the juvenile materials wt %) represents
the originalfeaturesof classIII fragis obtainedby carefullycrushingjuvenile clasts(dotted
mentshangingin the atmosphereduring the climactic
curve)andalsoby calculatingfromtwo-dimensional
size
distributionin thin sections(dashedcurve). Details of Plinian phase. On the other hand, the proportionof
plagioclase
in classII (Xn/Sn) is •55 wt % in layerC1
the method to calculate from 2-D size distribution to 3(Table3). The
D sizedistributionwill be describedelsewhere(M. Ohno and •56 wt % in layerC2, respectively
and T. Koyaguchi,manuscriptin preparation,2001).
total amountsof layer C1 and layer C2 estimatedfrom
KOYAGUCHI AND OHNO: RECONSTRUCTION OF ERUPTION COLUMNS, 2
these values are listed in Table 5. The ranges of the
estimates, in which the preferable release altitudes and
the effect of regional wind are taken into account, are
0
! i i ,
! ! i !
! , ! ,
6527
ß ! ! !
i ! !
determinedfrom the resultsin Tables 5 and B3 (com-
pareFigure7). They are 1.0-1.9 x 10TMkg for layerC1
and 1.1-2.0 x 1012kg for layerC2. Theseresultsimply
that the proportionsof classIII fragmentsare 48-57%
for layer C1 and 51-60% for layer C2. Becausethe estimates of this method are sensitive to the proportion of
plagioclasein classIII fragments, we took into account
the analytical error of XRD (+2 wt %) in determining T
the above ranges.
_E- 20 ...................................
•,'...........
The
estimates
of the total
mass on the basis of the
15 ..................
:...................
:..................
•.............
-f....:.............
10
proportionof plagioclasein the fine-ashlayer (2.1-3.9
x10TMkg as a whole)are consistent
with the previous
estimateswhich are obtained by applying the empirical
thickness-distancerelationship to the distal area includ-
ing the SouthChinaSea(rangingfrom 3 to 4.8 x 1012
kg) [Scottet al., 1991,1996; Wiesnerel al., 1995; Wiesnet and Wang,1996; Paladio-Melosantos
et al., 1996].
Consideringthat these estimatesrely on different basic
ideas, the agreement of the results of the two methods
is surprising.
We emphasizeagain that the above estimatesare sensitive to the proportion of plagioclasein classIII fragments. If we use the proportion of plagioclasein layer
B (35 q-2 wt %) insteadof that of the fine ash in layer
C2, the estimatesof total massbecome3.3-10.1 x 1012
kg. The origin of the variation in proportion of plagioclasebetween layers B and C2 is unclear at present.
0
0
50
100
150
200
250
Velocity (m/s)
Figure 12, Velocity structuresof rising eruption
columnswhich explain the granu]ometricdata of layer
Cl (so]ia cues)
C: (ashea cues).
explanation see text.
intensity of the eruption was highest during the first
half of the climactic phase and declined with time from
layer C1 to layer C2. Judgingfrom the high proportion
of very fine particles,most of the juvenile materials can
Size distributions of fine ash in layer C2 and those in be assumedto have thermally equilibrated with the atlayer B, which were measuredutilizing the scattering mosphereimmediately. Substitutingthe magma temof a laser beam through a stream of particles, do not perature of 1000 to 1100 K, which has been estimated
depend on the distance from the vent or whether they from two-oxide geothermometryand stability field of
1993;Imai et al., 1993, 1996]
belongto layer B or C2. This observationsuggeststhat amphibole[Rutherford,
(for
critical
assessment
of
theseestimations,see Koythe effectof sortingis limited for the fine ashin thesedeaguchi
[1996]),
and
the
typical
value (1100 J/(K kg))
posits. Although SEM observationshowsno systematic
of
the
specific
heat
of
magma
[
Woods
andKienle, 1994]
differencein shapeof fragmentsbetweenthe two stratiinto
equation
(28)
of
paper
1,
we
can
estimatemagma
graphic units, the fragmentation mechanismmay have
dischargerate from the rate of thermal release to be
been different betweenbefore and during the climactic
Plinian phase. In order to verify the present method,
further study on the origin of class III fragments is
necessary(M. Ohno and T. Koyaguchi,manuscriptin
preparation,2001). The aboveresultsalso containerrors causedby the overestimationof the bulk density of
deposit(at mosta few tensof percent);however,this effect would be within
the errors due to the uncertainties
of the proportion of plagioclasein classIII fragments.
6.0-11 x108kg/s for layerC1 and2.5-4.3 x108kg/s
for layer C2. These results and the estimates of the total •mount of the ejecta yield the effective duration of
the eruptionsof 0.4-0.6 hour for layer C1 and 1.1-1.4
hours for layer C2. The estimates of the effective duration can be assessed on the basis of the real-time
obser-
vations(section4).
Possiblevelocitystructuresof risingeruption columns,
whichexplainthe abovemagmadischargerates and the
grain-size distributions at the top of the eruption column (Figure 9), are calculatedon the basisof the fluid
If the effect of the entrainment
of the ambient air at
dynamicsmodelby Woods[1988](Figure 12). It is reathe top of the cloud can be assumedto be negligible sonableto assumethat the terminalfall velocityof the
[e.g., Sparkset al., 1997],the rate of thermal energy coursersideof cutoffsizeof classII fragmentsroughly
release can be estimated from the volumetric expan- represents
the minimumrisingvelocityof the eruption
sion rate of the umbrella cloud to be -•5-9 X10 TMW
column.The velocitystructuresare characterizedby a
for layer C1 and -•2-3.5 X10TMW for layer C2 using distinctdeceleration
in the gasthrust region;the minequation(27) of paper 1. This result suggeststhat the imumvelocityat the top of the gasthrustr.egion
is
3.5.
Dynamics of Eruption
Column
6528
KOYAGUCHI AND OHNO: RECONSTRUCTION
OF ERUPTION COLUMNS, 2
Table 6. Comparison Between Granulometric Estimates and Other Observations
GranulometricEstimate (This Study)
Other Observation
Volumetric
FlowRateI•, m3/s
5-
LayerC• 5 - 9 x 10TM
LayerC2 2 - 3.5 x 10TM
10 x 10TM•
MassDischarge
Rate1•, kg/s
6- 12 x 10s c
> 109d
LayerC• 6.0- 11 x l0 s b
LayerC2 2.5- 4.3 x l0 s b
Total Mass, kg
59-
LayerC• 1.0- 1.9(0.9) x 10• e
LayerC• 1.1- 2.0 (0.9) x 10• e
25 x 10• f
15 x 10•2 g
Duration, hours
LayerC• 0.4 - 0.6(0.3) e,h
LayerC• 1.1- 1.4(0.8) e,h
LayerC• 3.5 i
LayerC2 7 i
Minimum Rising Velocity,m/s
Layer C• 50 - 100
Layer C2 20- 50
supported by generation of pyrocalstic flow
aSatellitedata [Koyaguchiand Tokuno,1993;Holaseket al., 1996a].
bEstimate
fromgranulometric
1•.
Estimate from satellite 1•.
dEstimatefrom columnheightand cloudtop temperature[Holaseket al., 1996a;Koyaguchi,1996].
eNumbersin parenthesesare estimatesassumingthat all the plagioclasecrystalsbelongto classII.
fEstimatefrom satelliteimagesand the dynamicsmodel[Koyaguchi,1996].
gEstimatefrom columnheight [Holaseket al., 1996a].
hSli+III/M.
iEstimatefrom infrasonicdata [Tabira et al., 1996].
50-100 m/s for layer C1 and 20-50 m/s for layer C2.
4. Comparison
It is suggestedthat the condition of the eruption was
close to that of column collapse, particularly for the
Observations
With
Real-Time
The most usefuldata that can be directly compared
with
the presentestimationsare the satellite images
idea is supported by the fact that layer C2 locally conof
expanding
eruption cloud (for detailed description,
tains silt-sizeparticles, which may have originated from
see
Koyaguchi
and Tokuno[1993]and Holaseket al.
coignimbriteashclouds(Figure 1), and by stratigraphic
[1996a]).
The
climactic
phaseof the Pinatubo 1991
evidence that some pyroelastic flows are interbedded
eruptionof layer C2 [Bursik and Woods,1991]. This
in layersC1 and C2 in the proximalarea [Scottet al.,
A summary of the parameters of eruption column dynamics reconstructedby granulometric data is given on
the left-hand side of Table 6. In addition to these parameters we can calculate total height of the eruption
column, temperature of the cloud top, and velocity and
radius just after decompressionat the vent on the basis
of the fluid dynamicsmodels[e.g., Woods,1988](Table
7). For thesecalculationsthe water contentin magma
is assumedto be 6 wt % on the basisof the experimen-
Table 7. Calculated Parameters of Eruption Column
Dynamics Which Are ConsistentWith the Results in
Figure 12a
Column height, km
Altitude of NBL, km
Cloud top temperature, øC
Vent radius,
•m
aAll the calculations
Layer C•
Layer C2
34- 36
23 - 24
-92--84
29 - 30
21 - 22
-102- -98
610 - 680
435- 455
are based on the model of Woods
tal data by Rutherford[1993]. Accordingto extensive [1988]underthe tropicalconditionfor the magmatempernumericalstudiesof a wider rangeof parameters[e.g., ature of 1000 K, water contentof 6 wt %, and the magma
specificheat of 1100 J/(K kg).
Koyaguchi,1996],the quantitiesin Table 7 dependon
bRadiusof plume just after decompression
to I atm at
the assumedwater content in magma to a considerable the vent. This radius dependson assumedmagma water
extent.
content rather sensitively.
KOYAGUCHI AND OHNO' RECONSTRUCTION OF ERUPTION COLUMNS, 2
eruption started at 1342 LT (local Philippine time) of
June 15, judging from the fact that all the seismographs
were saturated at the time. A distinct disc-shapedcloud
appeared in the satellite images at 1440 LT. According to the eyewitnessaccounts, fine ash fall with rain
started in the morning and became heavy after 1400
LT, even in the upwind region. Intermittent lapilli fall
started between 1400 and 1445 LT, and it became very
heavy and continuousafter 1500 LT even in the upwind
region. Considering the eyewitnessaccounts and the
timescalefor pumice grains to reach the ground from
the bottom of the cloud, it is inferred that the giant
cloud observedfrom 1440 LT onward yielded the lapilli
6529
was higher than that of layer C2. However, the duration in which the strong infrasonicwaveswere observed
(•10 hours)are muchlongerthan the effectiveduration
which is estimatedby dividing the total amount of the
ejectaby the magmadischarge
rate (Table 6). The estimates of the total amount, and hencethe estimatesof
effectiveduration dependon the assumedproportion of
plagioclasein classIII fragments. If the proportion of
plagioclasein layer B is used instead of that of the fine
ash in layer C2, the estimates of the effective duration
increase up to 0.6-1.4 hours for layer C1 and 1.7-3.5
hours for layer C2; however,these values are still substantially shorter than the duration based on infrasonic
fall of layer C1 and layer C2 [Koyaguchiand Tokuno, observation.
1993].
There are several possible explanations for this disThe cloudexpandedup to 280km in diameter(60,000 crepancyas follows: (1) The intensity of infrasonic
km2) at 1440LT and400kmin diameter
(120,000
km2) waves may not represent the intensity of magma disat 1540LT. It expandedup to 250 km upwind until 1940 chargerate, (2) the total amount of the ejecta is un-
LT, covering
an areaof 300,000km2, andsubsequently,derestimated,and (3) the magmadischargerate, which
the east end of the cloud moved westward, at which is estimated from the volumetric expansionrate on the
time the cloud reacheda stagnationpoint upwind but basis of the fluid dynamicsmodel, is too high. These
continuedto grow downwindand crosswind.Average possibilities are assessedbelow.
The duration in which the eruption cloud continradial expansionvelocity of the giant cloud was up to
102m/s before1440LT and •14 m/s between1440 ued to expand upwind was •5 hours [Koyaguchiand
and 1540 LT. The thickness of the cloud is estimated
to be •3-6
Tokuno,1993;Holaseket al., 1996a].Considering
that
km at the initial stage of the expansion the cloud can continue to expand even after the sup-
[Koyaguchiand Tokuno,1993; Holaseket al., 1996a; ply at its source ceases, the effective duration of the
Koyaguchi,1996]. From the top view of the cloudand eruption which induced tephra fall in the upwind rethe thicknessthe volumetric expansionrate is estimated
to be 5-10 x101øm3/s.The present
granulometric
es-
gion should be shorter than 5 hours. If we adopt, for
example, the duration of the intensive infrasonic wave
timate agreeswith this satelliteobservation(Table 6). (3.5 hours)as the effectiveduration, it agreeswith the
Considering
the effectof changein cloudthickness(sec- result on the basis of our highest total mass estimation
tion 6.3 in paper1), the presentgranulometric
estimates using the upper bound of the proportion of plagioclase
of 1• maybe regarded
asan overestimation
by a few in classIII (i.e., 37 wt % in layer B).
tens of percent; however, this effect is within the errors
causedby other uncertaintiesand will not modify the
In the climactic phaseof the Pinatubo 1991 eruption,
P linian eruptions and pyroclastic flows are thought to
above conclusion.
have been synchronous
[e.g., Scott et al., 1996]. The
The granulometric estimates predict that the inten-
present methods may underestimate the total amount
sity of the eruption was highestat the initial stageand of ejecta which contributed to the dynamicsof eruption
declinedwith time. This time dependenceis also sup- cloud for such eruptions. Even if thermal energy was
ported by the satellite images. Dimensionalanalyses suppliedfrom coignimbritefine ash to the eruption colindicate that the radius of the umbrella cloud increases
umn as well as pyroclasts from the vent, the amount of
with timein proportion
to t2/a whenthe gravitycur- the coignimbrite ash cannot be countedby the present
rent of the umbrella cloud is maintainedby a steady method based on classII fragments. In order to assess
eruption[Holaseket al., 1996b;Sparkset al., 1997]. this possibility,thorough investigationof the pyroclasThe observedradius,on the other hand, increases.ap- tic flow depositsand coignimbriteash is necessary.
proximatelyin proportionto t •/2. The difference
in the
We anticipate that the third possibilitywould also be
rate of the increase in the radius of the cloud can be
important because the overestimation of magma discharge rate is a natural consequenceof the discrepexplainedby the decliningintensity of the eruption.
The changein the intensityof the eruption with time ancy betweenthe volumetric expansionrate of umbrella
wasobservedthroughreal-timemonitoringof infrasonic cloudsand the volumetric flow rate at NBL. Previously,
waves. Strong infrasonic waves due to a series of explosion were measured for >10 hours from •1400 LT
it has been commonly assumedthat entrainment of the
climacticeruption for 3.5 hours. These data are quali-
ics of the cloud top inevitably results in entrainment of
the ambient air at the edge of plume. After the plume
risesto NBL the plume keepsrising although subjected
ambientair at the cloudtop and/or the surfaceof the
[Tahiraet al., 1996]. The amplitudeof the infrasonic umbrellacloudis negligible[Bursik et al., 1992; Koywaveswas particularly high at the initial stageof the aguchi,1994;Sparkset al., 1997].However,the dynamtatively consistent with the conclusion drawn from the
granulometricdata that the expansionrate of layer C1
6530
KOYAGUCHI AND OHNO' RECONSTRUCTION OF ERUPTION COLUMNS, 2
to a downward gravitational force. The plume's momentum will carry it to a final height from which it
will slump back gravitationally toward NBL. According
to our preliminary laboratory experimentsin stratified
1.9
1.8
salty water and numericalstudies(Y. Ishimineand T.
Koyaguchi,manuscriptin preparation,2001), this overshoot induces strong oscillation of the umbrella cloud
near the edge of plume, which results in considerable
entrainment of surroundingfluid into the umbrella region. The expansionrate of the umbrella cloud therefore becomessubstantiallygreater than the volumetric
flow rate at NBL, which may be sufficient to explain
the overestimation of the magma dischargerate. Further study of the dynamics of the cloud top is still in
progress.
In addition to the above discrepancywe point out
that
there
seem to be some inconsistencies
between
the
1.7
1.6
1.,5
1.4 ....
0
••
5
....
6 10
a (x10-)
]
15
Figure B1. The variationof the averagestandarddeviation(for data from -2½ to 3½)as a functionof a for
layer C1. Seeequation(34) of paper 1 for the definition
estimatesbasedon eruption column height or cloud top of •.
temperature and those based on expansionrate of umbrella clouds. Infrared imagesindicate that the surface
temperature of the giant cloud was > -60øC and there of the umbrella cloud was 35 km at 1440 LT, and it sub-
wasa smallhot spot (a few tens of kilometersin diam- sequentlydecreased
downto 24 km in 2 hours[Holasek
eter) with temperatureup to • -30øC at the centerof et al., 1996a]. Other studiessuggestthat the altitude
the cloud at 1440 and 1540 LT. These temperature data,
as well as the width of the shadowonto the surrounding
white clouds,indicate that the total height of the cloud
reached •40 km at the climactic phase of the eruption
of the eastern edge of the umbrella cloud was 25 km at
1540 LT [Tanaka et al., 1991; Koyaguchiand Tokuno,
1993]. Taking the thicknessof the cloudinto account
(3-6 km), NBL at 1440 LT is estimatedto have been
(1540 LT) [Tokuno,1991a,1991b;Tanakaet al., 1991; higher than 29 km, which is substantiallygreater than
from1• on the basisof the fluid
Koyaguchiand Tokuno,1993;Holaseket al., 1996a]. A the valuepredicted
seriesof calculationswith a wide range of parameters on dynamicsmodel (seeFigure 7). The altitude of the top
the basisof the fluid dynamicsmodelby Woods[1988] oftheumbrella
cloudafter1540LT.(•-25km)isconsisindicated that these values of column height and cloud tent with the value predicted from V• and the present
top temperature can be explained only by a very high resultsof releasealtitude (22-25 km for layer C1 and
magmadischarge
rate (>10• kg/s) [Koyaguchi,
1996]. 20-22 km for layer C•), consideringthe thicknessof the
A similar inconsistencycan be found also in the es- cloud.
timation of altitude of the umbrella cloud. Analyses of
The above two discrepancieswould be explained by
the satellite imagessuggestthat the altitude of the top the fact that cloud height and cloud top temperature
respondinstantaneouslyto varying eruption rate, while
expansionrate of an umbrella cloud representstime avlOO
erage of varying eruption rate. In the Pinatubo case
the estimates based on the expansion rate of the um-o-- LayerC•
brella cloud may have failed to detect the most intense
!-i
-B - LayerC2
explosionat the beginningof the climactic phase. Although the presentmethodsare basedon expansionrate
of umbrella clouds,it is possibleto detect the presence
of short-termfluctuationsof eruptionrate; the granulometric data of layer C1 in the upwind region imply that
there was fluctuation in eruptive conditionsduring the
climacticphase(seesection3.2).
lO
.
1.5
.
,
ß
I
2
.
ß
.
.
I
2.5
.
.
,
,
I
3
.
ß
.
.
I
3.5
,
.
.
.
I
4
.
ß
5.
.
4.5
Conclusion
The agreement of the estimates of the volumetric expansion rate by the present method with the real-time
Figure A1. Relationship
betweenmassof plagioclasesatellite observations is remarkable. Some important
freecrystalsandsquare-root
of areasurrounded
by each features of eruption column dynamics such as decelercontourof the isoplethmapsfor layerC1 (circles)and ation in the gas thrust region have been successfully
layer C• (squares).
reconstructed. It is important to bear in mind that the
(isopleth
area)ø'$(x 104 km)
KOYAGUCHI
AND OHNO: RECONSTRUCTION
present method is applicable to caseswhere the radial
expansion rate of umbrella clouds largely exceedsthe
effect of wind. The above agreementsare partly due to
the fact that the intensity of the Pinatubo 1991 eruption
was strong enoughto satisfy this condition.
The largest sourceof errors in the present methods
would be the estimation of total mass of the ejects.
The result is sensitiveto the proportion of fragmented
crystals in class III fragments. It is essential to understand the mechanismsto generate fine ash during
explosiveeruptions in order to improve the accuracy of
the present method.
One of the most serious discrepanciesbetween the
granulometric estimates and the real-time observations
is that of the effectiveduration of eruption (or magma
OF ERUPTION
COLUMNS, 2
6531
Table B2. Total Amount of Class II Fragmentsand
Class II PlagioclaseAfter Correction of the Effect of
Regional Wind a
Layer C1
20 km
25 km
Layer C2
30 km
20 km
25 km
30 km
6.0
7.0
Class H Fragments
5.1
5.6
(0.14)
(0.15)
6.2
(0.16)
5.3
(0.060) (0.066) (0.071)
Class H PlagioclaseFree Crystals
2.7
3.0
3.4
2.9
3.3
3.9
aNumbersin parenthesesindicate the amount of pumice
thanclass
II plagioclase
($p).In unitsof x1011kg;
dischargerate). Judgingby the agreementin the es- larger
c•-- 5 x 10-6 m -1.
timates of the expansion rate between the two independent methods, we anticipate that the origin of the
deviation would lie in modeling that connectsthe dynamicsof eruption columnsto the dynamicsof umbrella
clouds,rather than the dispersalmodel of the umbrella
clouds itself. The effect of atmospheric entrainment at
the cloud top is consideredto be a significant sourceof
the deviation. Alternatively, contemporaneousPlinian
activity and generation of pyroclastic flows in the climactic eruption may explain this discrepancy. These
effects should also be examined
in the future.
Finally,we pointout that if intensityof eruptionfluctuates with time, the resultsof instantaneousobservations such as cloud height in satellite images do not
alwaysagreewith the averagefeaturesof the eruption
estimatedby the presentmethods. The presentmethods can, however,qualitatively detect the presenceof
fluctuations of eruption rate.
where k is a constant determined by the isopleth map
in the accessibleregion. In more general, the distance,
r, can be replaced by the square-rootof the area of the
isopleth contour. The total mass of the crystals is then
obtained
from
XT -
X(r)d(7rr2).
(A2)
Figure A1 showsthe relationship between the mass of
plagioclasefree crystals and the square-rootof the area
of the isopleth contour for layers C• and C2. The total
amounts of the plagioclasefree crystals on the basis of
theserelationships
are 1.8 x 1011kg for layer C• and
1.2 x 10TMkg for layer C2. Theseresultsare slightly
smaller than the presentestimationsapplying equation
(22) of paper I to plagioclasecrystals(seeTables3 and
B2). Koyaguchi[1994]provedthat when the assumptions of the tephra dispersal model for class II holds,
the empirical relationshipof the exponential decreasing
Appendix A' Comparison With
Fierstein
and Nathenson's
Method
behavior (equation (A1)) can be extrapolatedtoward
FiefsteinandNathenson
[1992]proposed
a methodto infinite distance for a specificinitial grain size, which
estimate the total amount of ejecta in which the total is similar to a lognormaldistribution with a• •- 2.5.
amount of crystalsare determinedby an empiricalex- The discrepancyof the two methods may be partly attrapolationand then the crystalconcentrationmethod tributed to the fact that the grain-size distribution of
is applied. In their method the relationshipbetween plagioclasefree crystals is slightly deviated from the
the massof free crystalsper unit area, X(r), and the specificgrain-size distribution in this case.
distance, r, are given by
X(r) = X(0)exp(-kr),
(A1)
Appendix B' Effect of Regional Wind
In this appendix we crudely evaluate the effect of regional wind on the basisof the approximation presented
Table B1. Volumetric
Expansion
Rate l•wAfter Cor- in section6.2 of paper 1. The least squaresmethod on
rectionof the Effect of RegionalWinda
the basisof equation(35) in paper 1 wasperformedfor
AssumedAltitude, km
Layer C1
Layer C2
20
25
30
4.3 x 101ø
5.9 x 101ø
7.7 x 101ø
2.1 X 1010
2.8 x 101ø
3.7 x 101ø
SinmS/s;c•= 5 x 10-6 m-1.
various(• from0 to 15 x 10-6 m-• (seepaper1 for the
definition of (•). The effect of the regionalwind would
be evaluated by the average standard deviation of the
data (for data set from -2q• to 3q•)as a function of c•
(Figure B 1).
The standard deviation decreaseswith the increasing
(•, and it has a minimumvaluearound(• = 9 x 10-6
6532
KOYAGUCHI
AND OHNO: RECONSTRUCTION
Table B3. Total Amount of Ejecta After Correction
of the Effect of RegionalWind a
Layer C1
20 km
25 km
Layer C2
30 km
20 km
25 km
30 km
All the PlagioclasePhenocrystsBelong to Class H
6.9
7.5
8.4
7.4
8.4
9.8
(26)
(26)
(25)
(28)
(28)
(29)
Proportion of Plagioclasein ClassIII Fragmentsof 27 wt •o
11
12
13
12
13
16
(52)
(52)
(51)
(54)
(54)
(55)
Proportion of Plagioclasein ClassIII Fragmentsof 25 wt •o
9.8
11
12
11
12
14
(49)
(48)
(48)
(50)
(51)
(52)
Proportion of Plagioclasein ClassIII Fragmentsof 29 wt •o
12
13
14
13
15
17
(56)
(56)
(55)
(58)
(58)
(59)
aNumbers in parenthesesindicate the fraction of classIII
fragments
(wt %). In unitsof x 10TMkg;c•= 5 x 10-6 m-1
OF ERUPTION
COLUMNS, 2
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Bursik, M. I., and A. W. Woods, Buoyant, superbuoyant
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Bursik, M. I., R. S. J. Sparks, J. S. Gilbert, and S. N. Carey,
Sedimentation of tephra by volcanic plumes, I, Theory
and its comparisonwith a study of the Fogo A Plinian
deposit, Sao Miguel (Azores), Bull. Volcanol.,5•, 329344, 1992.
David, C. P. C., R. G. Dulce, D. D. Nalasco-Javier, L. R.
Zamoras, F. T. Jumawan, and C. G. Newhall, Changing
proportionsof two pumice types from the June 15, 1991,
eruption of Mount Pinatubo, in Fire and Mud: Eruptions
and Lahars of Mount Pinatubo, Philippines,edited by C.
G. Newhall and R. S. Punongbayan,pp. 681-685, Univ.
of Wash. Press, Seattle, 1996.
Fierstein, J., and M. Nathenson, Another look at the calculation of fallout tephra volumes, Bull. Volcanol., 5•,
156-167, 1992.
Hoblitt, R. P., E. W. Wolfe, W. E. Scott, M. R. Couchman,
J. S. Pallister, and D. Javier, The preclimacticeruptions
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Univ. of Wash. Press, Seattle, 1996.
Holasek, R. E., S. Self, and A. W. Woods, Satellite observations and interpretation of the 1991 Mount Pinatubo
eruption plumes, J. Geophys. Res., 101, 27,635-27,655,
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m-1
Holasek, R. E., A. W. Woods, and S. Self, Experiments on
gas-ashseparation processesin volcanic umbrella plumes,
J. Volcanol. Geotherm. Res., 70, 169-181, 1996b.
The value of a corresponds
to wind velocityof Imai, A., E. L. Listanco,and T. Fujii, Petrologicand sul-
•030m/sforanumbrella
cloud
of1••05x 1010
m3/sand
5 km thick, which is slightly greater than the meteorologicaldata; however,we must be carefulin interpreting
this result, becausethe approximationof equation(33)
of paper I is no longerrelevantfor large r (more than
severaltensof kilometers)
whena > 10x 10-6 m-1 and
so the minimum total error may not accurately represent the best estimation.
The
conclusion
that
we can
safely derive from these considerationswould be that
the effect of regional wind is present and that a may be
aslargeas 5 x 10-6 m-1.
The model parametersfor a - 5 x 10-6 m-1 are
listed in Tables B1, B2, and B3, which correspond to
Tables 1, 3, and 5, respectively. Without the correction
on the effectsof regional wind, the expansionrate and
the total amount of ejecta may be overestimated by
severaltens of percent. These effectsare therefore taken
into accountin determiningthe preferablerangesof the
estimates
in section
3.
Acknowledgments.
Discussionswith Y. Ishimine and
T. Kurihara were fruitful for the development of some of
the ideas presented here. We also thank T. Kawahara for
his assistanceof sieving analyses. Commentsby S. Self and
two anonymous reviewers greatly improved the paper.
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